LMFDB - Embedded newform 546.2.bw.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.37659 + 1.05119i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(3.72584 + 0.998336i) q^{5} +(1.37166 + 1.05761i) q^{6} +(-1.75384 - 1.98092i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.789991 - 2.89412i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.37659 + 1.05119i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(3.72584 + 0.998336i) q^{5} +(1.37166 + 1.05761i) q^{6} +(-1.75384 - 1.98092i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.789991 - 2.89412i) q^{9} -3.85727i q^{10} +(-2.65109 - 2.65109i) q^{11} +(0.666564 - 1.59865i) q^{12} +(3.53597 + 0.704936i) q^{13} +(-1.45950 + 2.20678i) q^{14} +(-6.17839 + 2.54228i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.429068 + 0.743168i) q^{17} +(-2.99997 - 0.0140200i) q^{18} +(3.04123 + 3.04123i) q^{19} +(-3.72584 + 0.998336i) q^{20} +(4.49664 + 0.883296i) q^{21} +(-1.87460 + 3.24691i) q^{22} +(2.53923 - 4.39808i) q^{23} +(-1.71670 - 0.230090i) q^{24} +(8.55508 + 4.93928i) q^{25} +(-0.234260 - 3.59793i) q^{26} +(1.95478 + 4.81444i) q^{27} +(2.50933 + 0.838611i) q^{28} +(2.97651 - 1.71849i) q^{29} +(4.05473 + 5.30988i) q^{30} +(5.31898 - 1.42522i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(6.43627 + 0.862655i) q^{33} +(0.606794 - 0.606794i) q^{34} +(-4.55689 - 9.13152i) q^{35} +(0.762906 + 2.90137i) q^{36} +(-1.48849 - 5.55513i) q^{37} +(2.15047 - 3.72473i) q^{38} +(-5.60859 + 2.74657i) q^{39} +(1.92864 + 3.34050i) q^{40} +(0.774470 + 0.207519i) q^{41} +(-0.310618 - 4.57204i) q^{42} +(1.15111 + 0.664595i) q^{43} +(3.62146 + 0.970367i) q^{44} +(5.83268 - 9.99434i) q^{45} +(-4.90542 - 1.31440i) q^{46} +(-1.51578 + 5.65698i) q^{47} +(0.222065 + 1.71776i) q^{48} +(-0.848111 + 6.94843i) q^{49} +(2.55676 - 9.54195i) q^{50} +(-1.37186 - 0.572003i) q^{51} +(-3.41471 + 1.15749i) q^{52} +(-4.07315 - 2.35163i) q^{53} +(4.14446 - 3.13424i) q^{54} +(-7.23086 - 12.5242i) q^{55} +(0.160574 - 2.64087i) q^{56} +(-7.38344 - 0.989606i) q^{57} +(-2.43031 - 2.43031i) q^{58} +(3.74289 - 13.9687i) q^{59} +(4.07951 - 5.29087i) q^{60} +3.10443 q^{61} +(-2.75331 - 4.76887i) q^{62} +(-7.11854 + 3.51090i) q^{63} +1.00000i q^{64} +(12.4707 + 6.15656i) q^{65} +(-0.832567 - 6.44023i) q^{66} +(9.89409 + 9.89409i) q^{67} +(-0.743168 - 0.429068i) q^{68} +(1.12775 + 8.72357i) q^{69} +(-7.64096 + 6.76503i) q^{70} +(0.326314 + 1.21782i) q^{71} +(2.60506 - 1.48784i) q^{72} +(-1.28743 - 4.80475i) q^{73} +(-4.98059 + 2.87555i) q^{74} +(-16.9690 + 2.19368i) q^{75} +(-4.15440 - 1.11317i) q^{76} +(-0.602025 + 9.90119i) q^{77} +(4.10460 + 4.70662i) q^{78} +(7.06620 + 12.2390i) q^{79} +(2.72750 - 2.72750i) q^{80} +(-7.75183 - 4.57265i) q^{81} -0.801790i q^{82} +(4.70571 - 4.70571i) q^{83} +(-4.33585 + 1.48336i) q^{84} +(0.856708 + 3.19728i) q^{85} +(0.344020 - 1.28390i) q^{86} +(-2.29097 + 5.49454i) q^{87} -3.74921i q^{88} +(1.13004 - 0.302794i) q^{89} +(-11.1634 - 3.04721i) q^{90} +(-4.80509 - 8.24082i) q^{91} +5.07846i q^{92} +(-5.82387 + 7.55321i) q^{93} +5.85654 q^{94} +(8.29497 + 14.3673i) q^{95} +(1.60175 - 0.659086i) q^{96} +(-3.55976 + 0.953834i) q^{97} +(6.93118 - 0.979174i) q^{98} +(-9.76690 + 5.57823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.37659	+	1.05119i	−0.794774	+	0.606906i
$3$	−1.37659	+	1.05119i	−0.794774	+	0.606906i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	3.72584	+	0.998336i	1.66625	+	0.446469i	0.964095	−	0.265558i	$-0.0855563\pi$
$5$	3.72584	+	0.998336i	1.66625	+	0.446469i	0.702151	+	0.712028i	$0.252223\pi$
$6$	1.37166	+	1.05761i	0.559978	+	0.431769i
$7$	−1.75384	−	1.98092i	−0.662888	−	0.748718i
$7$	−1.75384	−	1.98092i	−0.662888	−	0.748718i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.789991	−	2.89412i	0.263330	−	0.964706i
$10$		−	3.85727i		−	1.21978i
$11$	−2.65109	−	2.65109i	−0.799334	−	0.799334i	0.183657	−	0.982990i	$-0.441207\pi$
$11$	−2.65109	−	2.65109i	−0.799334	−	0.799334i	−0.982990	+	0.183657i	$0.941207\pi$
$12$	0.666564	−	1.59865i	0.192421	−	0.461491i
$13$	3.53597	+	0.704936i	0.980701	+	0.195514i
$13$	3.53597	+	0.704936i	0.980701	+	0.195514i
$14$	−1.45950	+	2.20678i	−0.390067	+	0.589786i
$15$	−6.17839	+	2.54228i	−1.59525	+	0.656413i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.429068	+	0.743168i	0.104064	+	0.180245i	0.913356	−	0.407163i	$-0.133482\pi$
$17$	0.429068	+	0.743168i	0.104064	+	0.180245i	−0.809291	+	0.587408i	$0.800149\pi$
$18$	−2.99997	−	0.0140200i	−0.707099	−	0.00330455i
$19$	3.04123	+	3.04123i	0.697706	+	0.697706i	0.963915	−	0.266209i	$-0.0857712\pi$
$19$	3.04123	+	3.04123i	0.697706	+	0.697706i	−0.266209	+	0.963915i	$0.585771\pi$
$20$	−3.72584	+	0.998336i	−0.833123	+	0.223235i
$21$	4.49664	+	0.883296i	0.981248	+	0.192751i
$22$	−1.87460	+	3.24691i	−0.399667	+	0.692243i
$23$	2.53923	−	4.39808i	0.529467	−	0.917063i	−0.469943	−	0.882697i	$-0.655725\pi$
$23$	2.53923	−	4.39808i	0.529467	−	0.917063i	0.999409	−	0.0343661i	$-0.0109412\pi$
$24$	−1.71670	−	0.230090i	−0.350420	−	0.0469669i
$25$	8.55508	+	4.93928i	1.71102	+	0.987856i
$26$	−0.234260	−	3.59793i	−0.0459422	−	0.705613i
$27$	1.95478	+	4.81444i	0.376198	+	0.926539i
$28$	2.50933	+	0.838611i	0.474219	+	0.158483i
$29$	2.97651	−	1.71849i	0.552724	−	0.319115i	−0.197496	−	0.980304i	$-0.563281\pi$
$29$	2.97651	−	1.71849i	0.552724	−	0.319115i	0.750220	+	0.661188i	$0.229948\pi$
$30$	4.05473	+	5.30988i	0.740290	+	0.969447i
$31$	5.31898	−	1.42522i	0.955318	−	0.255977i	0.252700	−	0.967545i	$-0.418681\pi$
$31$	5.31898	−	1.42522i	0.955318	−	0.255977i	0.702617	+	0.711568i	$0.252015\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	6.43627	+	0.862655i	1.12041	+	0.150169i
$34$	0.606794	−	0.606794i	0.104064	−	0.104064i
$35$	−4.55689	−	9.13152i	−0.770255	−	1.54351i
$36$	0.762906	+	2.90137i	0.127151	+	0.483562i
$37$	−1.48849	−	5.55513i	−0.244707	−	0.913258i	−0.973531	−	0.228557i	$-0.926599\pi$
$37$	−1.48849	−	5.55513i	−0.244707	−	0.913258i	0.728824	−	0.684701i	$-0.240067\pi$
$38$	2.15047	−	3.72473i	0.348853	−	0.604231i
$39$	−5.60859	+	2.74657i	−0.898094	+	0.439804i
$40$	1.92864	+	3.34050i	0.304944	+	0.528179i
$41$	0.774470	+	0.207519i	0.120952	+	0.0324090i	0.318787	−	0.947826i	$-0.396724\pi$
$41$	0.774470	+	0.207519i	0.120952	+	0.0324090i	−0.197835	+	0.980235i	$0.563391\pi$
$42$	−0.310618	−	4.57204i	−0.0479294	−	0.705481i
$43$	1.15111	+	0.664595i	0.175543	+	0.101350i	0.585197	−	0.810891i	$-0.301017\pi$
$43$	1.15111	+	0.664595i	0.175543	+	0.101350i	−0.409654	+	0.912241i	$0.634351\pi$
$44$	3.62146	+	0.970367i	0.545955	+	0.146288i
$45$	5.83268	−	9.99434i	0.869485	−	1.48987i
$46$	−4.90542	−	1.31440i	−0.723265	−	0.193798i
$47$	−1.51578	+	5.65698i	−0.221100	+	0.825156i	0.762830	+	0.646599i	$0.223809\pi$
$47$	−1.51578	+	5.65698i	−0.221100	+	0.825156i	−0.983930	+	0.178557i	$0.942857\pi$
$48$	0.222065	+	1.71776i	0.0320523	+	0.247937i
$49$	−0.848111	+	6.94843i	−0.121159	+	0.992633i
$50$	2.55676	−	9.54195i	0.361580	−	1.34944i
$51$	−1.37186	−	0.572003i	−0.192099	−	0.0800965i
$52$	−3.41471	+	1.15749i	−0.473534	+	0.160515i
$53$	−4.07315	−	2.35163i	−0.559490	−	0.323022i	0.193451	−	0.981110i	$-0.438032\pi$
$53$	−4.07315	−	2.35163i	−0.559490	−	0.323022i	−0.752941	+	0.658088i	$0.771365\pi$
$54$	4.14446	−	3.13424i	0.563989	−	0.426516i
$55$	−7.23086	−	12.5242i	−0.975009	−	1.68877i
$56$	0.160574	−	2.64087i	0.0214576	−	0.352902i
$57$	−7.38344	−	0.989606i	−0.977961	−	0.131076i
$58$	−2.43031	−	2.43031i	−0.319115	−	0.319115i
$59$	3.74289	−	13.9687i	0.487283	−	1.81857i	−0.0822676	−	0.996610i	$-0.526216\pi$
$59$	3.74289	−	13.9687i	0.487283	−	1.81857i	0.569551	−	0.821956i	$-0.307117\pi$
$60$	4.07951	−	5.29087i	0.526662	−	0.683048i
$61$	3.10443			0.397481			0.198741	−	0.980052i	$-0.436315\pi$
$61$	3.10443			0.397481			0.198741	+	0.980052i	$0.436315\pi$
$62$	−2.75331	−	4.76887i	−0.349671	−	0.605647i
$63$	−7.11854	+	3.51090i	−0.896852	+	0.442332i
$64$			1.00000i			0.125000i
$65$	12.4707	+	6.15656i	1.54680	+	0.763627i
$66$	−0.832567	−	6.44023i	−0.102482	−	0.792737i
$67$	9.89409	+	9.89409i	1.20876	+	1.20876i	0.971430	+	0.237325i	$0.0762707\pi$
$67$	9.89409	+	9.89409i	1.20876	+	1.20876i	0.237325	+	0.971430i	$0.423729\pi$
$68$	−0.743168	−	0.429068i	−0.0901223	−	0.0520321i
$69$	1.12775	+	8.72357i	0.135765	+	1.05019i
$70$	−7.64096	+	6.76503i	−0.913269	+	0.808576i
$71$	0.326314	+	1.21782i	0.0387264	+	0.144529i	0.982582	−	0.185829i	$-0.0594971\pi$
$71$	0.326314	+	1.21782i	0.0387264	+	0.144529i	−0.943856	+	0.330358i	$0.892830\pi$
$72$	2.60506	−	1.48784i	0.307009	−	0.175344i
$73$	−1.28743	−	4.80475i	−0.150682	−	0.562353i	−0.999437	−	0.0335659i	$-0.989314\pi$
$73$	−1.28743	−	4.80475i	−0.150682	−	0.562353i	0.848754	−	0.528787i	$-0.177353\pi$
$74$	−4.98059	+	2.87555i	−0.578982	+	0.334276i
$75$	−16.9690	+	2.19368i	−1.95941	+	0.253304i
$76$	−4.15440	−	1.11317i	−0.476542	−	0.127689i
$77$	−0.602025	+	9.90119i	−0.0686071	+	1.12834i
$78$	4.10460	+	4.70662i	0.464754	+	0.532920i
$79$	7.06620	+	12.2390i	0.795010	+	1.37700i	0.922833	+	0.385200i	$0.125868\pi$
$79$	7.06620	+	12.2390i	0.795010	+	1.37700i	−0.127823	+	0.991797i	$0.540799\pi$
$80$	2.72750	−	2.72750i	0.304944	−	0.304944i
$81$	−7.75183	−	4.57265i	−0.861314	−	0.508073i
$82$		−	0.801790i		−	0.0885429i
$83$	4.70571	−	4.70571i	0.516519	−	0.516519i	−0.399998	−	0.916516i	$-0.630989\pi$
$83$	4.70571	−	4.70571i	0.516519	−	0.516519i	0.916516	+	0.399998i	$0.130989\pi$
$84$	−4.33585	+	1.48336i	−0.473080	+	0.161848i
$85$	0.856708	+	3.19728i	0.0929230	+	0.346793i
$86$	0.344020	−	1.28390i	0.0370966	−	0.138446i
$87$	−2.29097	+	5.49454i	−0.245617	+	0.589076i
$88$		−	3.74921i		−	0.399667i
$89$	1.13004	−	0.302794i	0.119784	−	0.0320961i	−0.198429	−	0.980115i	$-0.563584\pi$
$89$	1.13004	−	0.302794i	0.119784	−	0.0320961i	0.318213	+	0.948019i	$0.396917\pi$
$90$	−11.1634	−	3.04721i	−1.17673	−	0.321204i
$91$	−4.80509	−	8.24082i	−0.503710	−	0.863873i
$92$			5.07846i			0.529467i
$93$	−5.82387	+	7.55321i	−0.603908	+	0.783231i
$94$	5.85654			0.604056
$95$	8.29497	+	14.3673i	0.851046	+	1.47405i
$96$	1.60175	−	0.659086i	0.163478	−	0.0672677i
$97$	−3.55976	+	0.953834i	−0.361439	+	0.0968472i	−0.434968	−	0.900446i	$-0.643240\pi$
$97$	−3.55976	+	0.953834i	−0.361439	+	0.0968472i	0.0735295	+	0.997293i	$0.476574\pi$
$98$	6.93118	−	0.979174i	0.700155	−	0.0989116i
$99$	−9.76690	+	5.57823i	−0.981611	+	0.560633i
$100$	−9.87856			−0.987856
$101$	−17.2461			−1.71605			−0.858025	−	0.513608i	$-0.828309\pi$
$101$	−17.2461			−1.71605			−0.858025	+	0.513608i	$0.828309\pi$
$102$	−0.197449	+	1.47316i	−0.0195503	+	0.145865i
$103$	−16.2604	+	9.38793i	−1.60218	+	0.925021i	−0.611133	+	0.791528i	$0.709286\pi$
$103$	−16.2604	+	9.38793i	−1.60218	+	0.925021i	−0.991050	+	0.133493i	$0.957381\pi$
$104$	2.00184	+	2.99877i	0.196297	+	0.294054i
$105$	15.8719	+	7.78018i	1.54894	+	0.759268i
$106$	−1.21730	+	4.54301i	−0.118234	+	0.441256i
$107$	−13.4340	−	7.75615i	−1.29872	−	0.749815i	−0.318535	−	0.947911i	$-0.603191\pi$
$107$	−13.4340	−	7.75615i	−1.29872	−	0.749815i	−0.980183	+	0.198096i	$0.936524\pi$
$108$	−4.10011	−	3.19204i	−0.394533	−	0.307154i
$109$	1.40866	−	0.377448i	0.134925	−	0.0361530i	−0.190725	−	0.981644i	$-0.561084\pi$
$109$	1.40866	−	0.377448i	0.134925	−	0.0361530i	0.325649	+	0.945491i	$0.394417\pi$
$110$	−10.2260	+	10.2260i	−0.975009	+	0.975009i
$111$	7.88855	+	6.08244i	0.748748	+	0.577319i
$112$	−2.59245	+	0.528406i	−0.244963	+	0.0499297i
$113$	−6.29558	−	3.63476i	−0.592239	−	0.341929i	0.173743	−	0.984791i	$-0.444414\pi$
$113$	−6.29558	−	3.63476i	−0.592239	−	0.341929i	−0.765982	+	0.642862i	$0.777747\pi$
$114$	0.955089	+	7.38798i	0.0894523	+	0.691948i
$115$	13.8515	−	13.8515i	1.29166	−	1.29166i
$116$	−1.71849	+	2.97651i	−0.159558	+	0.276362i
$117$	4.83355	−	9.67661i	0.446862	−	0.894603i
$118$	−14.4614			−1.33128
$119$	0.719642	−	2.15335i	0.0659695	−	0.197397i
$120$	−6.16644	−	2.57112i	−0.562917	−	0.234710i
$121$			3.05656i			0.277869i
$122$	−0.803485	−	2.99865i	−0.0727441	−	0.271485i
$123$	−1.28427	+	0.528449i	−0.115799	+	0.0476486i
$124$	−3.89377	+	3.89377i	−0.349671	+	0.349671i
$125$	13.3063	+	13.3063i	1.19015	+	1.19015i
$126$	5.23368	+	5.96729i	0.466253	+	0.531609i
$127$	−2.86221	+	1.65250i	−0.253980	+	0.146636i	−0.621585	−	0.783346i	$-0.713511\pi$
$127$	−2.86221	+	1.65250i	−0.253980	+	0.146636i	0.367605	+	0.929982i	$0.380178\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−2.28323	+	0.295166i	−0.201027	+	0.0259880i
$130$	2.71913	−	13.6392i	0.238483	−	1.19624i
$131$	10.0080	−	5.77814i	0.874406	−	0.504839i	0.00559642	−	0.999984i	$-0.498219\pi$
$131$	10.0080	−	5.77814i	0.874406	−	0.504839i	0.868810	+	0.495146i	$0.164885\pi$
$132$	−6.00530	+	2.47105i	−0.522694	+	0.215077i
$133$	0.690620	−	11.3583i	0.0598844	−	0.984887i
$134$	6.99618	−	12.1177i	0.604378	−	1.04681i
$135$	2.47677	+	19.8894i	0.213166	+	1.71180i
$136$	−0.222102	+	0.828896i	−0.0190451	+	0.0710772i
$137$	−5.11382	+	19.0851i	−0.436904	+	1.63055i	0.299566	+	0.954076i	$0.403158\pi$
$137$	−5.11382	+	19.0851i	−0.436904	+	1.63055i	−0.736470	+	0.676471i	$0.763509\pi$
$138$	8.13444	−	3.34715i	0.692449	−	0.284928i
$139$	−2.39445	+	4.14730i	−0.203094	+	0.351770i	−0.949524	−	0.313695i	$-0.898433\pi$
$139$	−2.39445	+	4.14730i	−0.203094	+	0.351770i	0.746430	+	0.665464i	$0.231766\pi$
$140$	8.51214	+	5.62968i	0.719407	+	0.475795i
$141$	−3.85996	−	9.38072i	−0.325068	−	0.789999i
$142$	1.09187	−	0.630391i	0.0916276	−	0.0529012i
$143$	−7.50532	−	11.2430i	−0.627627	−	0.940188i
$144$	−2.11138	−	2.13121i	−0.175949	−	0.177601i
$145$	12.8056	−	3.43126i	1.06345	−	0.284950i
$146$	−4.30782	+	2.48712i	−0.356518	+	0.205836i
$147$	−6.13664	−	10.4567i	−0.506141	−	0.862451i
$148$	4.06664	+	4.06664i	0.334276	+	0.334276i
$149$	−4.60973	+	4.60973i	−0.377644	+	0.377644i	−0.870251	−	0.492608i	$-0.836044\pi$
$149$	−4.60973	+	4.60973i	−0.377644	+	0.377644i	0.492608	+	0.870251i	$0.336044\pi$
$150$	6.51082	+	15.8230i	0.531606	+	1.29194i
$151$	−4.51053	−	16.8335i	−0.367062	−	1.36989i	−0.864604	−	0.502454i	$-0.832431\pi$
$151$	−4.51053	−	16.8335i	−0.367062	−	1.36989i	0.497542	−	0.867440i	$-0.334236\pi$
$152$			4.30095i			0.348853i
$153$	2.48977	−	0.654678i	0.201286	−	0.0529275i
$154$	9.71963	−	1.98110i	0.783230	−	0.159642i
$155$	21.2405			1.70608
$156$	3.48390	−	5.18290i	0.278935	−	0.414964i
$157$	−10.1263	+	17.5393i	−0.808171	+	1.39979i	0.105959	+	0.994370i	$0.466209\pi$
$157$	−10.1263	+	17.5393i	−0.808171	+	1.39979i	−0.914130	+	0.405422i	$0.867125\pi$
$158$	9.99312	−	9.99312i	0.795010	−	0.795010i
$159$	8.07907	−	1.04443i	0.640712	−	0.0828287i
$160$	−3.34050	−	1.92864i	−0.264089	−	0.152472i
$161$	−13.1657	+	2.68349i	−1.03760	+	0.211489i
$162$	−2.41052	+	8.67118i	−0.189389	+	0.681272i
$163$	−4.35488	+	4.35488i	−0.341101	+	0.341101i	−0.856781	−	0.515680i	$-0.827539\pi$
$163$	−4.35488	+	4.35488i	−0.341101	+	0.341101i	0.515680	+	0.856781i	$0.327539\pi$
$164$	−0.774470	+	0.207519i	−0.0604759	+	0.0162045i
$165$	23.1193	+	9.63967i	1.79983	+	0.750447i
$166$	−5.76329	−	3.32744i	−0.447318	−	0.258259i
$167$	−4.58101	+	17.0966i	−0.354489	+	1.32297i	0.526637	+	0.850091i	$0.323453\pi$
$167$	−4.58101	+	17.0966i	−0.354489	+	1.32297i	−0.881126	+	0.472882i	$0.843214\pi$
$168$	2.55502	+	3.80419i	0.197124	+	0.293500i
$169$	12.0061	+	4.98526i	0.923549	+	0.383481i
$170$	2.86660	−	1.65503i	0.219858	−	0.126935i
$171$	11.2042	−	6.39913i	0.856808	−	0.489354i
$172$	−1.32919			−0.101350
$173$	−2.37018			−0.180201			−0.0901007	−	0.995933i	$-0.528719\pi$
$173$	−2.37018			−0.180201			−0.0901007	+	0.995933i	$0.528719\pi$
$174$	5.90026	+	0.790814i	0.447297	+	0.0599515i
$175$	−5.21989	−	25.6096i	−0.394587	−	1.93591i
$176$	−3.62146	+	0.970367i	−0.272978	+	0.0731441i
$177$	9.53133	+	23.1636i	0.716419	+	1.74108i
$178$	−0.584954	−	1.01317i	−0.0438441	−	0.0759403i
$179$	−9.40766			−0.703162			−0.351581	−	0.936157i	$-0.614356\pi$
$179$	−9.40766			−0.703162			−0.351581	+	0.936157i	$0.614356\pi$
$180$	−0.0540790	+	11.5717i	−0.00403081	+	0.862503i
$181$		−	24.3790i		−	1.81207i	−0.423198	−	0.906037i	$-0.639093\pi$
$181$		−	24.3790i		−	1.81207i	0.423198	−	0.906037i	$-0.360907\pi$
$182$	−6.71637	+	6.77424i	−0.497851	+	0.502140i
$183$	−4.27352	+	3.26335i	−0.315908	+	0.241234i
$184$	4.90542	−	1.31440i	0.361632	−	0.0968991i
$185$		−	22.1835i		−	1.63097i
$186$	8.80317	+	3.67052i	0.645480	+	0.269135i
$187$	0.832707	−	3.10770i	0.0608935	−	0.227258i
$188$	−1.51578	−	5.65698i	−0.110550	−	0.412578i
$189$	6.10867	−	12.3160i	0.444340	−	0.895858i
$190$	11.7309	−	11.7309i	0.851046	−	0.851046i
$191$		−	16.2518i		−	1.17594i	−0.808883	−	0.587969i	$-0.799928\pi$
$191$		−	16.2518i		−	1.17594i	0.808883	−	0.587969i	$-0.200072\pi$
$192$	−1.05119	−	1.37659i	−0.0758632	−	0.0993467i
$193$	1.72992	−	1.72992i	0.124523	−	0.124523i	−0.642099	−	0.766622i	$-0.721936\pi$
$193$	1.72992	−	1.72992i	0.124523	−	0.124523i	0.766622	+	0.642099i	$0.221936\pi$
$194$	1.84267	+	3.19159i	0.132296	+	0.229143i
$195$	−23.6387	+	4.63404i	−1.69280	+	0.331850i
$196$	−2.73973	−	6.44157i	−0.195695	−	0.460112i
$197$	−17.2752	−	4.62888i	−1.23081	−	0.329794i	−0.415914	−	0.909404i	$-0.636538\pi$
$197$	−17.2752	−	4.62888i	−1.23081	−	0.329794i	−0.814894	+	0.579610i	$0.803205\pi$
$198$	7.91602	+	7.99035i	0.562567	+	0.567850i
$199$	−7.65170	+	4.41771i	−0.542415	+	0.313163i	−0.746057	−	0.665882i	$-0.768055\pi$
$199$	−7.65170	+	4.41771i	−0.542415	+	0.313163i	0.203642	+	0.979045i	$0.434722\pi$
$200$	2.55676	+	9.54195i	0.180790	+	0.674718i
$201$	−24.0207	−	3.21950i	−1.69429	−	0.227086i
$202$	4.46362	+	16.6584i	0.314059	+	1.17208i
$203$	−8.62451	−	2.88229i	−0.605322	−	0.202297i
$204$	1.47407	−	0.190562i	0.103205	−	0.0133420i
$205$	2.67838	+	1.54636i	0.187066	+	0.108003i
$206$	13.2765	+	13.2765i	0.925021	+	0.925021i
$207$	−10.7226	−	10.8233i	−0.745271	−	0.752270i
$208$	2.37848	−	2.70977i	0.164918	−	0.187889i
$209$		−	16.1252i		−	1.11540i
$210$	3.40711	−	17.3448i	0.235113	−	1.19690i
$211$	9.92000	+	17.1820i	0.682921	+	1.18285i	0.974085	+	0.226181i	$0.0726241\pi$
$211$	9.92000	+	17.1820i	0.682921	+	1.18285i	−0.291164	+	0.956673i	$0.594043\pi$
$212$	4.70327			0.323022
$213$	−1.72937	−	1.33342i	−0.118494	−	0.0913644i
$214$	−4.01488	+	14.9837i	−0.274451	+	1.02427i
$215$	3.62537	+	3.62537i	0.247248	+	0.247248i
$216$	−2.02208	+	4.78656i	−0.137585	+	0.325684i
$217$	−12.1519	−	8.03690i	−0.824923	−	0.545580i
$218$	−0.729174	−	1.26297i	−0.0493859	−	0.0855389i
$219$	6.82297	+	5.26083i	0.461054	+	0.355494i
$220$	12.5242	+	7.23086i	0.844383	+	0.487505i
$221$	0.993285	+	2.93028i	0.0668156	+	0.197112i
$222$	3.83347	−	9.19400i	0.257286	−	0.617061i
$223$	1.25289	−	4.67584i	0.0838995	−	0.313117i	−0.911204	−	0.411955i	$-0.864846\pi$
$223$	1.25289	−	4.67584i	0.0838995	−	0.313117i	0.995104	+	0.0988382i	$0.0315126\pi$
$224$	1.18138	+	2.36735i	0.0789340	+	0.158175i
$225$	21.0533	−	20.8574i	1.40355	−	1.39049i
$226$	−1.88149	+	7.02181i	−0.125155	+	0.467084i
$227$	−9.71058	−	2.60194i	−0.644514	−	0.172697i	−0.0782667	−	0.996932i	$-0.524939\pi$
$227$	−9.71058	−	2.60194i	−0.644514	−	0.172697i	−0.566247	+	0.824235i	$0.691605\pi$
$228$	6.88905	−	2.83470i	0.456238	−	0.187732i
$229$	1.65457	+	0.443341i	0.109337	+	0.0292968i	0.313073	−	0.949729i	$-0.398642\pi$
$229$	1.65457	+	0.443341i	0.109337	+	0.0292968i	−0.203736	+	0.979026i	$0.565308\pi$
$230$	−16.9646	−	9.79451i	−1.11861	−	0.645831i
$231$	−9.57931	−	14.2627i	−0.630272	−	0.938417i
$232$	3.31987	+	0.889555i	0.217960	+	0.0584022i
$233$	7.49512	+	12.9819i	0.491022	+	0.850474i	0.999947	−	0.0103366i	$-0.00329030\pi$
$233$	7.49512	+	12.9819i	0.491022	+	0.850474i	−0.508925	+	0.860811i	$0.669957\pi$
$234$	−10.5979	−	2.16436i	−0.692807	−	0.141488i
$235$	−11.2951	+	19.5638i	−0.736814	+	1.27620i
$236$	3.74289	+	13.9687i	0.243642	+	0.909283i
$237$	−22.5928	−	9.42016i	−1.46756	−	0.611905i
$238$	−2.26623	−	0.137794i	−0.146898	−	0.00893187i
$239$	7.39507	−	7.39507i	0.478347	−	0.478347i	−0.426256	−	0.904603i	$-0.640168\pi$
$239$	7.39507	−	7.39507i	0.478347	−	0.478347i	0.904603	+	0.426256i	$0.140168\pi$
$240$	−0.887520	+	6.62178i	−0.0572892	+	0.427434i
$241$	−7.98507	−	2.13959i	−0.514364	−	0.137823i	−0.00770536	−	0.999970i	$-0.502453\pi$
$241$	−7.98507	−	2.13959i	−0.514364	−	0.137823i	−0.506658	+	0.862147i	$0.669119\pi$
$242$	2.95241	−	0.791097i	0.189788	−	0.0508536i
$243$	15.4778	−	1.85400i	0.992902	−	0.118934i
$244$	−2.68851	+	1.55221i	−0.172114	+	0.0993703i
$245$	−10.0968	+	25.0420i	−0.645060	+	1.59988i
$246$	0.842835	+	1.10373i	0.0537372	+	0.0703716i
$247$	8.60982	+	12.8976i	0.547830	+	0.820652i
$248$	4.76887	+	2.75331i	0.302824	+	0.174835i
$249$	−1.53122	+	11.4244i	−0.0970371	+	0.723993i
$250$	9.40896	−	16.2968i	0.595075	−	1.03070i
$251$	0.193651	−	0.335414i	0.0122232	−	0.0211711i	−0.859849	−	0.510548i	$-0.829442\pi$
$251$	0.193651	−	0.335414i	0.0122232	−	0.0211711i	0.872072	+	0.489377i	$0.162776\pi$
$252$	4.40939	−	6.59980i	0.277765	−	0.415748i
$253$	−18.3914	+	4.92797i	−1.15626	+	0.309819i
$254$	2.33699	+	2.33699i	0.146636	+	0.146636i
$255$	−4.54029	−	3.50077i	−0.284324	−	0.219227i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.8686	−	24.0211i	0.865100	−	1.49840i	−0.00184764	−	0.999998i	$-0.500588\pi$
$257$	13.8686	−	24.0211i	0.865100	−	1.49840i	0.866948	−	0.498399i	$-0.166079\pi$
$258$	0.876051	+	2.12903i	0.0545406	+	0.132548i
$259$	−8.39371	+	12.6914i	−0.521560	+	0.788604i
$260$	−13.8782	+	0.903606i	−0.860690	+	0.0560393i
$261$	−2.62209	−	9.97196i	−0.162303	−	0.617249i
$262$	−8.17153	−	8.17153i	−0.504839	−	0.504839i
$263$			9.29775i			0.573324i	0.958032	+	0.286662i	$0.0925457\pi$
$263$			9.29775i			0.573324i	−0.958032	+	0.286662i	$0.907454\pi$
$264$	3.94114	+	5.16112i	0.242560	+	0.317645i
$265$	−12.8282	−	12.8282i	−0.788029	−	0.788029i
$266$	−11.1500	+	2.27265i	−0.683650	+	0.139345i
$267$	−1.23731	+	1.60472i	−0.0757222	+	0.0982071i
$268$	−13.5156	−	3.62149i	−0.825595	−	0.221218i
$269$	12.8317	−	7.40838i	0.782362	−	0.451697i	−0.0549045	−	0.998492i	$-0.517485\pi$
$269$	12.8317	−	7.40838i	0.782362	−	0.451697i	0.837267	+	0.546795i	$0.184152\pi$
$270$	18.5706	−	7.54012i	1.13017	−	0.458877i
$271$	7.75450	+	28.9402i	0.471052	+	1.75799i	0.636001	+	0.771688i	$0.280587\pi$
$271$	7.75450	+	28.9402i	0.471052	+	1.75799i	−0.164949	+	0.986302i	$0.552746\pi$
$272$	0.858136			0.0520321
$273$	15.2773	+	6.29315i	0.924625	+	0.380879i
$274$	19.7583			1.19364
$275$	−9.58582	−	35.7748i	−0.578047	−	2.15730i
$276$	−5.33844	−	6.99096i	−0.321336	−	0.420806i
$277$	−16.0694	+	9.27766i	−0.965515	+	0.557441i	−0.897866	−	0.440269i	$-0.854883\pi$
$277$	−16.0694	+	9.27766i	−0.965515	+	0.557441i	−0.0676493	+	0.997709i	$0.521550\pi$
$278$	4.62572	+	1.23946i	0.277432	+	0.0743377i
$279$	0.0772028	−	16.5197i	0.00462201	−	0.989007i
$280$	3.23475	−	9.67917i	0.193313	−	0.578441i
$281$	19.6555	+	19.6555i	1.17255	+	1.17255i	0.981600	+	0.190951i	$0.0611570\pi$
$281$	19.6555	+	19.6555i	1.17255	+	1.17255i	0.190951	+	0.981600i	$0.438843\pi$
$282$	−8.06204	+	6.15635i	−0.480088	+	0.366605i
$283$			22.2456i			1.32236i	0.750227	+	0.661181i	$0.229944\pi$
$283$			22.2456i			1.32236i	−0.750227	+	0.661181i	$0.770056\pi$
$284$	−0.891507	−	0.891507i	−0.0529012	−	0.0529012i
$285$	−26.5216	−	11.0583i	−1.57100	−	0.655035i
$286$	−8.91740	+	10.1595i	−0.527297	+	0.600743i
$287$	−0.947216	−	1.89812i	−0.0559124	−	0.112042i
$288$	−1.51213	+	2.59104i	−0.0891028	+	0.152678i
$289$	8.13180	−	14.0847i	0.478341	−	0.828511i
$290$	−6.62868	−	11.4812i	−0.389250	−	0.674200i
$291$	3.89766	−	5.05502i	0.228485	−	0.296331i
$292$	3.51732	+	3.51732i	0.205836	+	0.205836i
$293$	0.436492	−	0.116958i	0.0255001	−	0.00683274i	−0.246046	−	0.969258i	$-0.579132\pi$
$293$	0.436492	−	0.116958i	0.0255001	−	0.00683274i	0.271547	+	0.962425i	$0.412465\pi$
$294$	−8.51208	+	8.63392i	−0.496434	+	0.503540i
$295$	27.8909	−	48.3084i	1.62387	−	2.81262i
$296$	2.87555	−	4.98059i	0.167138	−	0.289491i
$297$	7.58122	−	17.9458i	0.439907	−	1.04132i
$298$	5.64574	+	3.25957i	0.327049	+	0.188822i
$299$	12.0790	−	13.7615i	0.698547	−	0.795846i
$300$	13.5987	−	10.3843i	0.785122	−	0.599535i
$301$	−0.702353	−	3.44586i	−0.0404829	−	0.198616i
$302$	−15.0925	+	8.71368i	−0.868478	+	0.501416i
$303$	23.7408	−	18.1290i	1.36387	−	1.04148i
$304$	4.15440	−	1.11317i	0.238271	−	0.0638445i
$305$	11.5666	+	3.09926i	0.662302	+	0.177463i
$306$	−1.27677	−	2.23549i	−0.0729881	−	0.127795i
$307$	−1.88568	+	1.88568i	−0.107622	+	0.107622i	−0.758867	−	0.651245i	$-0.774247\pi$
$307$	−1.88568	+	1.88568i	−0.107622	+	0.107622i	0.651245	+	0.758867i	$0.274247\pi$
$308$	−4.42922	−	8.87569i	−0.252379	−	0.505739i
$309$	12.5153	−	30.0161i	0.711972	−	1.70756i
$310$	−5.49745	−	20.5168i	−0.312234	−	1.16527i
$311$	6.16349	−	10.6755i	0.349499	−	0.605351i	−0.636661	−	0.771144i	$-0.719685\pi$
$311$	6.16349	−	10.6755i	0.349499	−	0.605351i	0.986161	+	0.165793i	$0.0530183\pi$
$312$	−5.90800	−	2.02375i	−0.334474	−	0.114572i
$313$	3.28838	+	5.69564i	0.185870	+	0.321937i	0.943869	−	0.330319i	$-0.107156\pi$
$313$	3.28838	+	5.69564i	0.185870	+	0.321937i	−0.757999	+	0.652256i	$0.773823\pi$
$314$	19.5626	+	5.24178i	1.10398	+	0.295811i
$315$	−30.0276	+	5.97436i	−1.69186	+	0.336617i
$316$	−12.2390	−	7.06620i	−0.688499	−	0.397505i
$317$	−0.412915	−	0.110640i	−0.0231916	−	0.00621418i	0.247205	−	0.968963i	$-0.420488\pi$
$317$	−0.412915	−	0.110640i	−0.0231916	−	0.00621418i	−0.270396	+	0.962749i	$0.587155\pi$
$318$	−3.09986	−	7.53346i	−0.173831	−	0.422456i
$319$	−12.4469	−	3.33513i	−0.696891	−	0.186731i
$320$	−0.998336	+	3.72584i	−0.0558087	+	0.208281i
$321$	26.6463	−	3.44473i	1.48725	−	0.192266i
$322$	5.99958	+	12.0225i	0.334343	+	0.669988i
$323$	−0.955250	+	3.56504i	−0.0531515	+	0.198364i
$324$	8.99961	+	0.0841191i	0.499978	+	0.00467329i
$325$	26.7686	+	23.4959i	1.48486	+	1.30332i
$326$	5.33362	+	3.07937i	0.295402	+	0.170550i
$327$	−1.54237	+	2.00036i	−0.0852932	+	0.110620i
$328$	0.400895	+	0.694371i	0.0221357	+	0.0383402i
$329$	13.8645	−	6.91878i	0.764374	−	0.381444i
$330$	3.32750	−	24.8264i	0.183173	−	1.36665i
$331$	−8.71729	−	8.71729i	−0.479145	−	0.479145i	0.425713	−	0.904858i	$-0.360023\pi$
$331$	−8.71729	−	8.71729i	−0.479145	−	0.479145i	−0.904858	+	0.425713i	$0.860023\pi$
$332$	−1.72241	+	6.42812i	−0.0945294	+	0.352789i
$333$	−17.2531	−	0.0806304i	−0.945464	−	0.00441852i
$334$	17.6997			0.968483
$335$	26.9862	+	46.7414i	1.47441	+	2.55376i
$336$	3.01328	−	3.45256i	0.164388	−	0.188352i
$337$		−	16.3884i		−	0.892732i	−0.894850	−	0.446366i	$-0.852718\pi$
$337$		−	16.3884i		−	0.892732i	0.894850	−	0.446366i	$-0.147282\pi$
$338$	1.70797	−	12.8873i	0.0929015	−	0.700977i
$339$	12.4873	−	1.61430i	0.678215	−	0.0876769i
$340$	−2.34057	−	2.34057i	−0.126935	−	0.126935i
$341$	−17.8795	−	10.3227i	−0.968229	−	0.559007i
$342$	−9.08095	−	9.16623i	−0.491042	−	0.495653i
$343$	15.2518	−	10.5064i	0.823517	−	0.567291i
$344$	0.344020	+	1.28390i	0.0185483	+	0.0692232i
$345$	−4.50724	+	33.6285i	−0.242662	+	1.81050i
$346$	0.613447	+	2.28942i	0.0329791	+	0.123080i
$347$	−9.98796	+	5.76655i	−0.536182	+	0.309565i	−0.743530	−	0.668702i	$-0.766850\pi$
$347$	−9.98796	+	5.76655i	−0.536182	+	0.309565i	0.207348	+	0.978267i	$0.433517\pi$
$348$	−0.763232	−	5.90389i	−0.0409135	−	0.316482i
$349$	28.2682	+	7.57445i	1.51316	+	0.405451i	0.917485	−	0.397771i	$-0.130216\pi$
$349$	28.2682	+	7.57445i	1.51316	+	0.405451i	0.595680	+	0.803222i	$0.296883\pi$
$350$	−23.3860	+	11.6703i	−1.25003	+	0.623803i
$351$	3.51817	+	18.4017i	0.187786	+	0.982210i
$352$	1.87460	+	3.24691i	0.0999167	+	0.173061i
$353$	−11.4105	+	11.4105i	−0.607322	+	0.607322i	−0.942245	−	0.334923i	$-0.891290\pi$
$353$	−11.4105	+	11.4105i	−0.607322	+	0.607322i	0.334923	+	0.942245i	$0.391290\pi$
$354$	19.9074	−	15.2017i	1.05807	−	0.807964i
$355$			4.86318i			0.258111i
$356$	−0.827250	+	0.827250i	−0.0438441	+	0.0438441i
$357$	1.27293	+	3.72075i	0.0673705	+	0.196923i
$358$	2.43488	+	9.08711i	0.128688	+	0.480268i
$359$	−2.15970	+	8.06012i	−0.113985	+	0.425397i	−0.999209	−	0.0397678i	$-0.987338\pi$
$359$	−2.15970	+	8.06012i	−0.113985	+	0.425397i	0.885224	+	0.465165i	$0.154005\pi$
$360$	11.1914	−	2.94274i	0.589838	−	0.155096i
$361$		−	0.501829i		−	0.0264121i
$362$	−23.5483	+	6.30974i	−1.23767	+	0.331633i
$363$	−3.21303	−	4.20763i	−0.168641	−	0.220843i
$364$	8.28174	+	4.73422i	0.434081	+	0.248140i
$365$		−	19.1870i		−	1.00429i
$366$	4.25822	+	3.28329i	0.222581	+	0.171620i
$367$	15.7591			0.822617			0.411309	−	0.911496i	$-0.365072\pi$
$367$	15.7591			0.822617			0.411309	+	0.911496i	$0.365072\pi$
$368$	−2.53923	−	4.39808i	−0.132367	−	0.229266i
$369$	1.21241	−	2.07747i	0.0631154	−	0.108149i
$370$	−21.4277	+	5.74152i	−1.11397	+	0.298488i
$371$	2.48524	+	12.1930i	0.129027	+	0.633028i
$372$	1.26702	−	9.45321i	0.0656918	−	0.490126i
$373$	−21.5208			−1.11430			−0.557152	−	0.830410i	$-0.688106\pi$
$373$	−21.5208			−1.11430			−0.557152	+	0.830410i	$0.688106\pi$
$374$	−3.21733			−0.166364
$375$	−32.3047	−	4.32982i	−1.66821	−	0.223591i
$376$	−5.07191	+	2.92827i	−0.261564	+	0.151014i
$377$	11.7363	−	3.97827i	0.604448	−	0.204891i
$378$	−13.4774	−	2.71290i	−0.693202	−	0.139537i
$379$	−3.78995	+	14.1443i	−0.194677	+	0.726544i	0.797674	+	0.603090i	$0.206064\pi$
$379$	−3.78995	+	14.1443i	−0.194677	+	0.726544i	−0.992350	+	0.123454i	$0.960603\pi$
$380$	−14.3673	−	8.29497i	−0.737027	−	0.425523i
$381$	2.20299	−	5.28354i	0.112863	−	0.270684i
$382$	−15.6980	+	4.20628i	−0.803181	+	0.215212i
$383$	−12.7850	+	12.7850i	−0.653286	+	0.653286i	−0.953783	−	0.300497i	$-0.902847\pi$
$383$	−12.7850	+	12.7850i	−0.653286	+	0.653286i	0.300497	+	0.953783i	$0.402847\pi$
$384$	−1.05761	+	1.37166i	−0.0539711	+	0.0699973i
$385$	−12.1278	+	36.2892i	−0.618088	+	1.84947i
$386$	−2.11871	−	1.22324i	−0.107840	−	0.0622613i
$387$	2.83279	−	2.80643i	0.143999	−	0.142659i
$388$	2.60592	−	2.60592i	0.132296	−	0.132296i
$389$	17.0678	−	29.5624i	0.865374	−	1.49887i	−0.00130104	−	0.999999i	$-0.500414\pi$
$389$	17.0678	−	29.5624i	0.865374	−	1.49887i	0.866675	−	0.498873i	$-0.166253\pi$
$390$	10.5943	+	21.6339i	0.536463	+	1.09547i
$391$	4.35801			0.220394
$392$	−5.51299	+	4.31358i	−0.278448	+	0.217869i
$393$	−7.70301	+	18.4745i	−0.388566	+	0.931915i
$394$			17.8846i			0.901014i
$395$	14.1089	+	52.6551i	0.709895	+	2.64936i
$396$	5.66927	−	9.71434i	0.284892	−	0.488164i
$397$	4.38709	−	4.38709i	0.220182	−	0.220182i	−0.588393	−	0.808575i	$-0.700239\pi$
$397$	4.38709	−	4.38709i	0.220182	−	0.220182i	0.808575	+	0.588393i	$0.200239\pi$
$398$	6.24759	+	6.24759i	0.313163	+	0.313163i
$399$	10.9890	+	16.3616i	0.550139	+	0.819106i
$400$	8.55508	−	4.93928i	0.427754	−	0.246964i
$401$	13.0832	−	3.50563i	0.653344	−	0.175063i	0.0831034	−	0.996541i	$-0.473517\pi$
$401$	13.0832	−	3.50563i	0.653344	−	0.175063i	0.570240	+	0.821478i	$0.306850\pi$
$402$	3.10721	+	24.0355i	0.154974	+	1.19878i
$403$	19.8124	−	1.28998i	0.986928	−	0.0642586i
$404$	14.9356	−	8.62305i	0.743072	−	0.429013i
$405$	−24.3170	−	24.7759i	−1.20832	−	1.23112i
$406$	−0.551889	+	9.07663i	−0.0273898	+	0.450465i
$407$	−10.7810	+	18.6733i	−0.534395	+	0.925600i
$408$	−0.565586	−	1.37452i	−0.0280007	−	0.0680489i
$409$	−3.97926	+	14.8508i	−0.196762	+	0.734324i	0.795042	+	0.606554i	$0.207449\pi$
$409$	−3.97926	+	14.8508i	−0.196762	+	0.734324i	−0.991804	+	0.127770i	$0.959218\pi$
$410$	0.800456	−	2.98734i	0.0395317	−	0.147534i
$411$	−13.0224	−	31.6479i	−0.642349	−	1.56107i
$412$	9.38793	−	16.2604i	0.462510	−	0.801091i
$413$	−34.2353	+	17.0844i	−1.68461	+	0.840668i
$414$	−7.67928	+	13.1585i	−0.377416	+	0.646705i
$415$	22.2306	−	12.8348i	1.09126	−	0.630037i
$416$	−3.23303	−	1.59609i	−0.158512	−	0.0782548i
$417$	−1.06344	−	8.22615i	−0.0520771	−	0.402836i
$418$	−15.5757	+	4.17350i	−0.761833	+	0.204132i
$419$	−19.8136	+	11.4394i	−0.967957	+	0.558850i	−0.898613	−	0.438742i	$-0.855424\pi$
$419$	−19.8136	+	11.4394i	−0.967957	+	0.558850i	−0.0693443	+	0.997593i	$0.522091\pi$
$420$	−17.6356	+	1.19814i	−0.860529	+	0.0584632i
$421$	15.0535	+	15.0535i	0.733661	+	0.733661i	0.971343	−	0.237682i	$-0.0763875\pi$
$421$	15.0535	+	15.0535i	0.733661	+	0.733661i	−0.237682	+	0.971343i	$0.576388\pi$
$422$	14.0290	−	14.0290i	0.682921	−	0.682921i
$423$	15.1745	+	8.85582i	0.737810	+	0.430585i
$424$	−1.21730	−	4.54301i	−0.0591171	−	0.220628i
$425$			8.47715i			0.411202i
$426$	−0.840392	+	2.01555i	−0.0407171	+	0.0976539i
$427$	−5.44466	−	6.14963i	−0.263486	−	0.297602i
$428$	15.5123			0.749815
$429$	22.1503	+	7.58747i	1.06943	+	0.366327i
$430$	2.56353	−	4.44016i	0.123624	−	0.214123i
$431$	−11.6481	+	11.6481i	−0.561072	+	0.561072i	−0.929612	−	0.368540i	$-0.879858\pi$
$431$	−11.6481	+	11.6481i	−0.561072	+	0.561072i	0.368540	+	0.929612i	$0.379858\pi$
$432$	5.14682	+	0.714331i	0.247626	+	0.0343682i
$433$	30.5376	+	17.6309i	1.46754	+	0.847287i	0.999340	−	0.0363331i	$-0.0115677\pi$
$433$	30.5376	+	17.6309i	1.46754	+	0.847287i	0.468204	+	0.883620i	$0.344901\pi$
$434$	−4.61791	+	13.8179i	−0.221667	+	0.663281i
$435$	−14.0212	+	18.1846i	−0.672264	+	0.871885i
$436$	−1.03121	+	1.03121i	−0.0493859	+	0.0493859i
$437$	21.0980	−	5.65318i	1.00925	−	0.270428i
$438$	3.31565	−	7.95209i	0.158428	−	0.379965i
$439$	−34.9853	−	20.1988i	−1.66976	−	0.964036i	−0.967766	−	0.251852i	$-0.918960\pi$
$439$	−34.9853	−	20.1988i	−1.66976	−	0.964036i	−0.701993	−	0.712184i	$-0.747706\pi$
$440$	3.74297	−	13.9689i	0.178439	−	0.665944i
$441$	19.4396	+	7.94373i	0.925694	+	0.378273i
$442$	2.57335	−	1.71785i	0.122402	−	0.0817099i
$443$	−14.1384	+	8.16280i	−0.671735	+	0.387826i	−0.796734	−	0.604330i	$-0.793441\pi$
$443$	−14.1384	+	8.16280i	−0.671735	+	0.387826i	0.124999	+	0.992157i	$0.460107\pi$
$444$	−9.87290	−	1.32327i	−0.468547	−	0.0627996i
$445$	4.51265			0.213920
$446$	−4.84078			−0.229218
$447$	1.49999	−	11.1914i	0.0709470	−	0.529335i
$448$	1.98092	−	1.75384i	0.0935898	−	0.0828610i
$449$	−10.2311	+	2.74141i	−0.482834	+	0.129375i	−0.492022	−	0.870583i	$-0.663742\pi$
$449$	−10.2311	+	2.74141i	−0.482834	+	0.129375i	0.00918765	+	0.999958i	$0.497075\pi$
$450$	−25.5957	−	14.9376i	−1.20659	−	0.704166i
$451$	−1.50304	−	2.60334i	−0.0707753	−	0.122586i
$452$	7.26951			0.341929
$453$	23.9044	+	18.4314i	1.12313	+	0.865983i
$454$			10.0531i			0.471817i
$455$	−9.67588	−	35.5011i	−0.453612	−	1.66432i
$456$	−4.52112	−	5.92064i	−0.211721	−	0.277259i
$457$	−1.54759	+	0.414676i	−0.0723932	+	0.0193977i	−0.294834	−	0.955549i	$-0.595264\pi$
$457$	−1.54759	+	0.414676i	−0.0723932	+	0.0193977i	0.222441	+	0.974946i	$0.428598\pi$
$458$		−	1.71294i		−	0.0800404i
$459$	−2.73920	+	3.51845i	−0.127855	+	0.164227i
$460$	−5.07001	+	18.9215i	−0.236391	+	0.882222i
$461$	2.74435	+	10.2421i	0.127817	+	0.477020i	0.999924	−	0.0122944i	$-0.00391354\pi$
$461$	2.74435	+	10.2421i	0.127817	+	0.477020i	−0.872107	+	0.489315i	$0.837247\pi$
$462$	−11.2974	+	12.9444i	−0.525603	+	0.602226i
$463$	13.8266	−	13.8266i	0.642577	−	0.642577i	−0.308611	−	0.951188i	$-0.599864\pi$
$463$	13.8266	−	13.8266i	0.642577	−	0.642577i	0.951188	+	0.308611i	$0.0998643\pi$
$464$		−	3.43698i		−	0.159558i
$465$	−29.2395	+	22.3279i	−1.35595	+	1.03543i
$466$	10.5997	−	10.5997i	0.491022	−	0.491022i
$467$	−8.30570	−	14.3859i	−0.384342	−	0.665699i	0.607336	−	0.794445i	$-0.292238\pi$
$467$	−8.30570	−	14.3859i	−0.384342	−	0.665699i	−0.991678	+	0.128746i	$0.958905\pi$
$468$	0.652330	+	10.7970i	0.0301540	+	0.499090i
$469$	2.24681	−	36.9520i	0.103748	−	1.70629i
$470$	21.8205	+	5.84679i	1.00651	+	0.269692i
$471$	−4.49741	−	34.7892i	−0.207230	−	1.60300i
$472$	12.5240	−	7.23072i	0.576462	−	0.332821i
$473$	−1.28980	−	4.81361i	−0.0593052	−	0.221330i
$474$	−3.25172	+	24.2611i	−0.149357	+	1.11435i
$475$	10.9965	+	41.0395i	0.504554	+	1.88302i
$476$	0.453444	+	2.22467i	0.0207836	+	0.101968i
$477$	−10.0237	+	9.93040i	−0.458952	+	0.454682i
$478$	−9.05707	−	5.22910i	−0.414261	−	0.239174i
$479$	−2.88625	−	2.88625i	−0.131876	−	0.131876i	0.638088	−	0.769964i	$-0.279726\pi$
$479$	−2.88625	−	2.88625i	−0.131876	−	0.131876i	−0.769964	+	0.638088i	$0.779726\pi$
$480$	6.62586	−	0.856564i	0.302428	−	0.0390966i
$481$	−1.34725	−	20.6920i	−0.0614294	−	0.943476i
$482$			8.26675i			0.376540i
$483$	15.3028	−	17.5337i	0.696303	−	0.797811i
$484$	−1.52828	−	2.64706i	−0.0694673	−	0.120321i
$485$	−14.2153			−0.645485
$486$	−5.79678	−	14.4706i	−0.262947	−	0.656398i
$487$	1.44456	−	5.39116i	0.0654591	−	0.244297i	−0.925442	−	0.378890i	$-0.876306\pi$
$487$	1.44456	−	5.39116i	0.0654591	−	0.244297i	0.990901	+	0.134593i	$0.0429726\pi$
$488$	2.19516	+	2.19516i	0.0993703	+	0.0993703i
$489$	1.41706	−	10.5727i	0.0640818	−	0.478114i
$490$	26.8020	+	3.27139i	1.21079	+	0.147787i
$491$	13.4071	+	23.2219i	0.605056	+	1.04799i	0.992043	+	0.125903i	$0.0401827\pi$
$491$	13.4071	+	23.2219i	0.605056	+	1.04799i	−0.386986	+	0.922085i	$0.626484\pi$
$492$	0.847984	−	1.09978i	0.0382301	−	0.0495821i
$493$	2.55425	+	1.47470i	0.115038	+	0.0664170i
$494$	10.2297	−	11.6546i	0.460256	−	0.524365i
$495$	−41.9589	+	11.0329i	−1.88591	+	0.495894i
$496$	1.42522	−	5.31898i	0.0639941	−	0.238829i
$497$	1.84011	−	2.78226i	0.0825402	−	0.124802i
$498$	11.4315	−	1.47781i	0.512256	−	0.0662224i
$499$	0.177961	−	0.664159i	0.00796662	−	0.0297318i	−0.961828	−	0.273654i	$-0.911768\pi$
$499$	0.177961	−	0.664159i	0.00796662	−	0.0297318i	0.969795	+	0.243922i	$0.0784342\pi$
$500$	−18.1767	−	4.87044i	−0.812888	−	0.217813i
$501$	−11.6656	−	28.3505i	−0.521181	−	1.26661i
$502$	−0.374105	−	0.100241i	−0.0166971	−	0.00447398i
$503$	5.03003	+	2.90409i	0.224278	+	0.129487i	0.607929	−	0.793991i	$-0.292000\pi$
$503$	5.03003	+	2.90409i	0.224278	+	0.129487i	−0.383652	+	0.923478i	$0.625334\pi$
$504$	−7.51615	−	2.55099i	−0.334796	−	0.113630i
$505$	−64.2562	−	17.2174i	−2.85936	−	0.766164i
$506$	9.52011	+	16.4893i	0.423221	+	0.733040i
$507$	−21.7680	+	5.75810i	−0.966749	+	0.255726i
$508$	1.65250	−	2.86221i	0.0733178	−	0.126990i
$509$	6.36355	+	23.7491i	0.282060	+	1.05266i	0.950961	+	0.309310i	$0.100098\pi$
$509$	6.36355	+	23.7491i	0.282060	+	1.05266i	−0.668902	+	0.743351i	$0.733235\pi$
$510$	−2.20637	+	5.29165i	−0.0976998	+	0.234318i
$511$	−7.25989	+	10.9770i	−0.321159	+	0.485596i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.69689	+	20.5868i	−0.383977	+	0.908928i
$514$	−26.7921	−	7.17892i	−1.18175	−	0.316649i
$515$	−69.9559	+	18.7446i	−3.08262	+	0.825987i
$516$	1.82975	−	1.39723i	0.0805502	−	0.0615098i
$517$	19.0157	−	10.9787i	0.836308	−	0.482842i
$518$	14.4314	+	4.82293i	0.634079	+	0.211907i
$519$	3.26276	−	2.49151i	0.143219	−	0.109365i
$520$	4.46476	+	13.1715i	0.195793	+	0.577606i
$521$	−4.56253	−	2.63418i	−0.199888	−	0.115405i	0.396715	−	0.917942i	$-0.370150\pi$
$521$	−4.56253	−	2.63418i	−0.199888	−	0.115405i	−0.596603	+	0.802536i	$0.703483\pi$
$522$	−8.95353	+	5.11368i	−0.391885	+	0.223820i
$523$	5.29803	−	9.17646i	0.231667	−	0.401258i	−0.726632	−	0.687027i	$-0.758915\pi$
$523$	5.29803	−	9.17646i	0.231667	−	0.401258i	0.958299	+	0.285768i	$0.0922488\pi$
$524$	−5.77814	+	10.0080i	−0.252419	+	0.437203i
$525$	34.1063	+	29.7668i	1.48852	+	1.29913i
$526$	8.98094	−	2.40644i	0.391588	−	0.104926i
$527$	3.34138	+	3.34138i	0.145553	+	0.145553i
$528$	3.96521	−	5.14264i	0.172564	−	0.223805i
$529$	−1.39540	−	2.41691i	−0.0606697	−	0.105083i
$530$	−9.07090	+	15.7113i	−0.394015	+	0.682453i
$531$	−37.4701	−	21.8675i	−1.62606	−	0.948969i
$532$	5.08104	+	10.1819i	0.220291	+	0.441440i
$533$	2.59221	+	1.27973i	0.112281	+	0.0554313i
$534$	1.87028	+	0.779819i	0.0809348	+	0.0337461i
$535$	−42.3098	−	42.3098i	−1.82921	−	1.82921i
$536$			13.9924i			0.604378i
$537$	12.9505	−	9.88926i	0.558854	−	0.426753i
$538$	−10.4770	−	10.4770i	−0.451697	−	0.451697i
$539$	20.6693	−	16.1725i	0.890292	−	0.696599i
$540$	−12.0896	−	15.9863i	−0.520255	−	0.687941i
$541$	−36.0291	−	9.65396i	−1.54901	−	0.415056i	−0.619846	−	0.784723i	$-0.712805\pi$
$541$	−36.0291	−	9.65396i	−1.54901	−	0.415056i	−0.929164	+	0.369667i	$0.879472\pi$
$542$	25.9470	−	14.9805i	1.11452	−	0.643469i
$543$	25.6270	+	33.5598i	1.09976	+	1.44019i
$544$	−0.222102	−	0.828896i	−0.00952254	−	0.0355386i
$545$	5.62525			0.240959
$546$	2.12465	−	16.3855i	0.0909268	−	0.701236i
$547$	−33.0367			−1.41255			−0.706274	−	0.707938i	$-0.749625\pi$
$547$	−33.0367			−1.41255			−0.706274	+	0.707938i	$0.749625\pi$
$548$	−5.11382	−	19.0851i	−0.218452	−	0.815273i
$549$	2.45247	−	8.98458i	0.104669	−	0.383452i
$550$	−32.0748	+	18.5184i	−1.36767	+	0.789626i
$551$	14.2786	+	3.82593i	0.608288	+	0.162990i
$552$	−5.37105	+	6.96593i	−0.228607	+	0.296490i
$553$	11.8516	−	35.4628i	0.503981	−	1.50803i
$554$	13.1206	+	13.1206i	0.557441	+	0.557441i
$555$	23.3192	+	30.5376i	0.989843	+	1.29625i
$556$		−	4.78889i		−	0.203094i
$557$	10.5786	+	10.5786i	0.448231	+	0.448231i	0.894766	−	0.446535i	$-0.147342\pi$
$557$	10.5786	+	10.5786i	0.448231	+	0.448231i	−0.446535	+	0.894766i	$0.647342\pi$
$558$	−15.9768	+	4.20103i	−0.676350	+	0.177844i
$559$	3.60180	+	3.16145i	0.152340	+	0.133715i
$560$	−10.1866	−	0.619377i	−0.430461	−	0.0261735i
$561$	2.12050	+	5.15336i	0.0895275	+	0.217575i
$562$	13.8986	−	24.0730i	0.586275	−	1.01546i
$563$	10.4516	+	18.1027i	0.440482	+	0.762938i	0.997725	−	0.0674118i	$-0.0214741\pi$
$563$	10.4516	+	18.1027i	0.440482	+	0.762938i	−0.557243	+	0.830350i	$0.688141\pi$
$564$	8.03319	+	6.19396i	0.338258	+	0.260813i
$565$	−19.8276	−	19.8276i	−0.834155	−	0.834155i
$566$	21.4876	−	5.75758i	0.903190	−	0.242009i
$567$	4.53737	+	23.3755i	0.190552	+	0.981677i
$568$	−0.630391	+	1.09187i	−0.0264506	+	0.0458138i
$569$	−8.09890	+	14.0277i	−0.339523	+	0.588072i	−0.984343	−	0.176263i	$-0.943599\pi$
$569$	−8.09890	+	14.0277i	−0.339523	+	0.588072i	0.644820	+	0.764335i	$0.276932\pi$
$570$	−3.81718	+	28.4799i	−0.159884	+	1.19289i
$571$	−20.6308	−	11.9112i	−0.863372	−	0.498468i	0.00176774	−	0.999998i	$-0.499437\pi$
$571$	−20.6308	−	11.9112i	−0.863372	−	0.498468i	−0.865140	+	0.501530i	$0.832771\pi$
$572$	12.1213	+	5.98408i	0.506817	+	0.250207i
$573$	17.0838	+	22.3720i	0.713684	+	0.934605i
$574$	−1.58828	+	1.40621i	−0.0662937	+	0.0586940i
$575$	43.4467	−	25.0840i	1.81185	−	1.04607i
$576$	2.89412	+	0.789991i	0.120588	+	0.0329163i
$577$	−14.6312	+	3.92043i	−0.609106	+	0.163209i	−0.550171	−	0.835052i	$-0.685437\pi$
$577$	−14.6312	+	3.92043i	−0.609106	+	0.163209i	−0.0589355	+	0.998262i	$0.518771\pi$
$578$	−15.7094	−	4.20933i	−0.653426	−	0.175085i
$579$	−0.562910	+	4.19987i	−0.0233938	+	0.174541i
$580$	−9.37437	+	9.37437i	−0.389250	+	0.389250i
$581$	−17.5747	−	1.06860i	−0.729121	−	0.0443330i
$582$	−5.89157	−	2.45651i	−0.244213	−	0.101826i
$583$	4.56389	+	17.0327i	0.189017	+	0.705422i
$584$	2.48712	−	4.30782i	0.102918	−	0.178259i
$585$	27.6695	−	31.2280i	1.14399	−	1.29112i
$586$	−0.225945	−	0.391348i	−0.00933370	−	0.0161664i
$587$	15.7504	+	4.22031i	0.650089	+	0.174191i	0.568769	−	0.822497i	$-0.307420\pi$
$587$	15.7504	+	4.22031i	0.650089	+	0.174191i	0.0813201	+	0.996688i	$0.474086\pi$
$588$	10.5428	+	5.98741i	0.434778	+	0.246917i
$589$	20.5107	+	11.8418i	0.845128	+	0.487935i
$590$	−53.8810	−	14.4374i	−2.21825	−	0.594377i
$591$	28.6467	−	11.7875i	1.17837	−	0.484873i
$592$	−5.55513	−	1.48849i	−0.228314	−	0.0611767i
$593$	7.08098	−	26.4266i	0.290781	−	1.08521i	−0.653730	−	0.756728i	$-0.726797\pi$
$593$	7.08098	−	26.4266i	0.290781	−	1.08521i	0.944511	−	0.328481i	$-0.106537\pi$
$594$	−19.2965	−	2.67817i	−0.791745	−	0.109887i
$595$	4.83103	−	7.30458i	0.198053	−	0.299458i
$596$	1.68728	−	6.29700i	0.0691136	−	0.257935i
$597$	5.88938	−	14.1248i	0.241036	−	0.578089i
$598$	−16.4188	−	8.10569i	−0.671416	−	0.331466i
$599$	−14.2351	−	8.21862i	−0.581629	−	0.335804i	0.180152	−	0.983639i	$-0.442341\pi$
$599$	−14.2351	−	8.21862i	−0.581629	−	0.335804i	−0.761780	+	0.647835i	$0.775674\pi$
$600$	−13.5500	−	10.4477i	−0.553178	−	0.426525i
$601$	0.289361	+	0.501188i	0.0118033	+	0.0204439i	0.871867	−	0.489743i	$-0.162909\pi$
$601$	0.289361	+	0.501188i	0.0118033	+	0.0204439i	−0.860063	+	0.510187i	$0.829576\pi$
$602$	−3.14666	+	1.57027i	−0.128248	+	0.0639996i
$603$	36.4509	−	20.8184i	1.48440	−	0.847791i
$604$	12.3230	+	12.3230i	0.501416	+	0.501416i
$605$	−3.05148	+	11.3883i	−0.124060	+	0.462999i
$606$	−23.6558	−	18.2397i	−0.960951	−	0.740937i
$607$	2.36201			0.0958710			0.0479355	−	0.998850i	$-0.484736\pi$
$607$	2.36201			0.0958710			0.0479355	+	0.998850i	$0.484736\pi$
$608$	−2.15047	−	3.72473i	−0.0872133	−	0.151058i
$609$	14.9022	−	5.09829i	0.603869	−	0.206593i
$610$		−	11.9746i		−	0.484838i
$611$	−9.34757	+	18.9344i	−0.378162	+	0.766003i
$612$	−1.82887	+	1.81185i	−0.0739277	+	0.0732399i
$613$	15.3281	+	15.3281i	0.619095	+	0.619095i	0.945299	−	0.326205i	$-0.105770\pi$
$613$	15.3281	+	15.3281i	0.619095	+	0.619095i	−0.326205	+	0.945299i	$0.605770\pi$
$614$	2.30948	+	1.33338i	0.0932031	+	0.0538108i
$615$	−5.31255	+	0.686785i	−0.214223	+	0.0276938i
$616$	−7.42689	+	6.57550i	−0.299238	+	0.264934i
$617$	0.234904	+	0.876672i	0.00945687	+	0.0352935i	0.970493	−	0.241129i	$-0.0775177\pi$
$617$	0.234904	+	0.876672i	0.00945687	+	0.0352935i	−0.961036	+	0.276423i	$0.910851\pi$
$618$	−32.2325	−	4.32014i	−1.29658	−	0.173782i
$619$	5.51391	+	20.5782i	0.221623	+	0.827107i	0.983730	+	0.179656i	$0.0574984\pi$
$619$	5.51391	+	20.5782i	0.221623	+	0.827107i	−0.762107	+	0.647451i	$0.775835\pi$
$620$	−18.3948	+	10.6203i	−0.738754	+	0.426520i
$621$	26.1379	+	3.62770i	1.04888	+	0.145575i
$622$	−11.9069	−	3.19046i	−0.477425	−	0.127926i
$623$	−2.58173	−	1.70748i	−0.103435	−	0.0684087i
$624$	−0.425694	+	6.23047i	−0.0170414	+	0.249419i
$625$	11.5965	+	20.0858i	0.463862	+	0.803432i
$626$	4.65047	−	4.65047i	0.185870	−	0.185870i
$627$	16.9506	+	22.1977i	0.676943	+	0.886491i
$628$		−	20.2527i		−	0.808171i
$629$	3.48973	−	3.48973i	0.139145	−	0.139145i
$630$	13.5425	+	27.4581i	0.539546	+	1.09396i
$631$	8.90953	+	33.2508i	0.354683	+	1.32369i	0.880883	+	0.473334i	$0.156950\pi$
$631$	8.90953	+	33.2508i	0.354683	+	1.32369i	−0.526200	+	0.850361i	$0.676384\pi$
$632$	−3.65773	+	13.6508i	−0.145497	+	0.543002i
$633$	−31.7173	−	13.2246i	−1.26065	−	0.525632i
$634$			0.427481i			0.0169775i
$635$	−12.3139	+	3.29950i	−0.488662	+	0.130937i
$636$	−6.47446	+	4.94404i	−0.256729	+	0.196044i
$637$	−7.89709	+	23.9716i	−0.312894	+	0.949788i
$638$			12.8859i			0.510159i
$639$	3.78230	+	0.0176762i	0.149626	+	0.000699259i
$640$	3.85727			0.152472
$641$	7.21354	+	12.4942i	0.284918	+	0.493492i	0.972589	−	0.232530i	$-0.0747003\pi$
$641$	7.21354	+	12.4942i	0.284918	+	0.493492i	−0.687671	+	0.726022i	$0.741367\pi$
$642$	−10.2239	−	24.8468i	−0.403507	−	0.980626i
$643$	25.2212	−	6.75799i	0.994626	−	0.266509i	0.275434	−	0.961320i	$-0.411179\pi$
$643$	25.2212	−	6.75799i	0.994626	−	0.266509i	0.719193	+	0.694811i	$0.244512\pi$
$644$	10.0600	−	8.90680i	0.396421	−	0.350977i
$645$	−8.80161	−	1.17968i	−0.346563	−	0.0464500i
$646$	3.69080			0.145213
$647$	−5.20845			−0.204765			−0.102383	−	0.994745i	$-0.532647\pi$
$647$	−5.20845			−0.204765			−0.102383	+	0.994745i	$0.532647\pi$
$648$	−2.24802	−	8.71472i	−0.0883104	−	0.342347i
$649$	−46.9550	+	27.1095i	−1.84314	+	1.06414i
$650$	15.7671	−	31.9377i	0.618436	−	1.25270i
$651$	25.1765	−	1.71046i	0.986743	−	0.0670381i
$652$	1.59400	−	5.94888i	0.0624257	−	0.232976i
$653$	−0.330355	−	0.190730i	−0.0129278	−	0.00746385i	0.493522	−	0.869733i	$-0.335709\pi$
$653$	−0.330355	−	0.190730i	−0.0129278	−	0.00746385i	−0.506450	+	0.862269i	$0.669043\pi$
$654$	2.33139	+	0.972083i	0.0911647	+	0.0380115i
$655$	43.0569	−	11.5371i	1.68237	−	0.450790i
$656$	0.566951	−	0.566951i	0.0221357	−	0.0221357i
$657$	−14.9226	−	0.0697389i	−0.582184	−	0.00272077i
$658$	−10.2714	−	11.6014i	−0.400422	−	0.452268i
$659$	−41.4586	−	23.9362i	−1.61500	−	0.932420i	−0.988187	−	0.153250i	$-0.951026\pi$
$659$	−41.4586	−	23.9362i	−1.61500	−	0.932420i	−0.626812	−	0.779170i	$-0.715641\pi$
$660$	−24.8417	+	3.21144i	−0.966962	+	0.125005i
$661$	−7.17493	+	7.17493i	−0.279073	+	0.279073i	−0.832739	−	0.553666i	$-0.813228\pi$
$661$	−7.17493	+	7.17493i	−0.279073	+	0.279073i	0.553666	+	0.832739i	$0.313228\pi$
$662$	−6.16405	+	10.6765i	−0.239573	+	0.414952i
$663$	−4.44763	−	2.98966i	−0.172732	−	0.116109i
$664$	6.65488			0.258259
$665$	13.9125	−	41.6296i	0.539504	−	1.61433i
$666$	4.38755	+	16.6861i	0.170014	+	0.646572i
$667$		−	17.4546i		−	0.675844i
$668$	−4.58101	−	17.0966i	−0.177245	−	0.661486i
$669$	3.19049	+	7.75373i	0.123352	+	0.299776i
$670$	38.1642	−	38.1642i	1.47441	−	1.47441i
$671$	−8.23012	−	8.23012i	−0.317720	−	0.317720i
$672$	−4.11481	−	2.01701i	−0.158732	−	0.0778080i
$673$	−43.7483	+	25.2581i	−1.68637	+	0.973628i	−0.729115	+	0.684391i	$0.760068\pi$
$673$	−43.7483	+	25.2581i	−1.68637	+	0.973628i	−0.957258	+	0.289237i	$0.906599\pi$
$674$	−15.8300	+	4.24163i	−0.609747	+	0.163381i
$675$	−7.05655	+	50.8431i	−0.271607	+	1.95695i
$676$	−12.8902	+	1.68571i	−0.495779	+	0.0648348i
$677$	−25.0911	+	14.4864i	−0.964331	+	0.556757i	−0.897503	−	0.441008i	$-0.854621\pi$
$677$	−25.0911	+	14.4864i	−0.964331	+	0.556757i	−0.0668277	+	0.997765i	$0.521288\pi$
$678$	−4.79124	−	11.6440i	−0.184006	−	0.447183i
$679$	8.13270	+	5.37873i	0.312105	+	0.206417i
$680$	−1.65503	+	2.86660i	−0.0634676	+	0.109929i
$681$	16.1026	−	6.62588i	0.617053	−	0.253904i
$682$	−5.34344	+	19.9420i	−0.204611	+	0.763618i
$683$	6.27561	−	23.4209i	0.240129	−	0.896175i	−0.735640	−	0.677373i	$-0.763118\pi$
$683$	6.27561	−	23.4209i	0.240129	−	0.896175i	0.975769	−	0.218802i	$-0.0702150\pi$
$684$	−6.50358	+	11.1439i	−0.248670	+	0.426099i
$685$	−38.1066	+	66.0025i	−1.45598	+	2.52183i
$686$	−14.0958	−	12.0128i	−0.538181	−	0.458651i
$687$	−2.74370	+	1.12897i	−0.104679	+	0.0430731i
$688$	1.15111	−	0.664595i	0.0438858	−	0.0253375i
$689$	−12.7448	−	11.1866i	−0.485537	−	0.426176i
$690$	33.6492	−	4.35003i	1.28100	−	0.165603i
$691$	23.2195	−	6.22164i	0.883310	−	0.236682i	0.211475	−	0.977383i	$-0.432173\pi$
$691$	23.2195	−	6.22164i	0.883310	−	0.236682i	0.671835	+	0.740701i	$0.265506\pi$
$692$	2.05264	−	1.18509i	0.0780295	−	0.0450503i
$693$	28.1796	+	9.56418i	1.07045	+	0.363313i
$694$	8.15514	+	8.15514i	0.309565	+	0.309565i
$695$	−13.0617	+	13.0617i	−0.495459	+	0.495459i
$696$	−5.50518	+	2.26526i	−0.208673	+	0.0858646i
$697$	0.178079	+	0.664601i	0.00674523	+	0.0251735i
$698$		−	29.2654i		−	1.10771i
$699$	−23.9642	−	9.99196i	−0.906409	−	0.377931i
$700$	17.3254	+	19.5687i	0.654838	+	0.739626i
$701$	−32.8796			−1.24185			−0.620923	−	0.783872i	$-0.713242\pi$
$701$	−32.8796			−1.24185			−0.620923	+	0.783872i	$0.713242\pi$
$702$	16.8641	−	8.16100i	0.636495	−	0.308017i
$703$	12.3676	−	21.4213i	0.466452	−	0.807919i
$704$	2.65109	−	2.65109i	0.0999167	−	0.0999167i
$705$	−5.01650	−	38.8046i	−0.188932	−	1.46147i
$706$	13.9750	+	8.06847i	0.525956	+	0.303661i
$707$	30.2468	+	34.1632i	1.13755	+	1.28484i
$708$	−19.8362	−	15.2946i	−0.745489	−	0.574807i
$709$	16.8613	−	16.8613i	0.633238	−	0.633238i	−0.315641	−	0.948879i	$-0.602219\pi$
$709$	16.8613	−	16.8613i	0.633238	−	0.633238i	0.948879	+	0.315641i	$0.102219\pi$
$710$	4.69747	−	1.25868i	0.176293	−	0.0472376i
$711$	41.0034	−	10.7817i	1.53775	−	0.404345i
$712$	1.01317	+	0.584954i	0.0379701	+	0.0219221i
$713$	7.23792	−	27.0123i	0.271062	−	1.01162i
$714$	3.26451	−	2.19256i	0.122171	−	0.0820544i
$715$	−16.7393	−	49.3825i	−0.626015	−	1.84680i
$716$	8.14728	−	4.70383i	0.304478	−	0.175790i
$717$	−2.40633	+	17.9536i	−0.0898660	+	0.670490i
$718$	8.34445			0.311412
$719$	26.6647			0.994424			0.497212	−	0.867629i	$-0.334357\pi$
$719$	26.6647			0.994424			0.497212	+	0.867629i	$0.334357\pi$
$720$	−5.73901	−	10.0484i	−0.213880	−	0.374482i
$721$	47.1148	+	15.7457i	1.75465	+	0.586399i
$722$	−0.484730	+	0.129883i	−0.0180398	+	0.00483374i
$723$	13.2413	−	5.44850i	0.492448	−	0.202632i
$724$	12.1895	+	21.1128i	0.453019	+	0.784651i
$725$	33.9524			1.26096
$726$	−3.23266	+	4.19257i	−0.119975	+	0.155601i
$727$		−	33.7416i		−	1.25141i	−0.780061	−	0.625703i	$-0.784812\pi$
$727$		−	33.7416i		−	1.25141i	0.780061	−	0.625703i	$-0.215188\pi$
$728$	2.42943	−	9.22485i	0.0900407	−	0.341896i
$729$	−19.3577	+	18.8223i	−0.716951	+	0.697124i
$730$	−18.5332	+	4.96596i	−0.685945	+	0.183799i
$731$			1.14063i			0.0421876i
$732$	2.06930	−	4.96290i	0.0764836	−	0.183434i
$733$	−10.2007	+	38.0696i	−0.376772	+	1.40613i	0.473966	+	0.880543i	$0.342822\pi$
$733$	−10.2007	+	38.0696i	−0.376772	+	1.40613i	−0.850738	+	0.525589i	$0.823845\pi$
$734$	−4.07875	−	15.2221i	−0.150549	−	0.561858i
$735$	−12.4249	−	45.0863i	−0.458298	−	1.66303i
$736$	−3.59102	+	3.59102i	−0.132367	+	0.132367i
$737$		−	52.4603i		−	1.93240i
$738$	−2.32047	−	0.633407i	−0.0854178	−	0.0233160i
$739$	10.9968	−	10.9968i	0.404525	−	0.404525i	−0.475299	−	0.879824i	$-0.657660\pi$
$739$	10.9968	−	10.9968i	0.404525	−	0.404525i	0.879824	+	0.475299i	$0.157660\pi$
$740$	11.0918	+	19.2115i	0.407742	+	0.706229i
$741$	−25.4100	−	8.70406i	−0.933460	−	0.319752i
$742$	11.1343	−	5.55633i	0.408753	−	0.203979i
$743$	2.98428	+	0.799634i	0.109482	+	0.0293357i	0.313144	−	0.949706i	$-0.398618\pi$
$743$	2.98428	+	0.799634i	0.109482	+	0.0293357i	−0.203662	+	0.979041i	$0.565284\pi$
$744$	−9.45903	+	1.22283i	−0.346785	+	0.0448310i
$745$	−21.7772	+	12.5730i	−0.797853	+	0.460641i
$746$	5.56999	+	20.7875i	0.203932	+	0.761084i
$747$	−9.90140	−	17.3363i	−0.362273	−	0.634303i
$748$	0.832707	+	3.10770i	0.0304468	+	0.113629i
$749$	8.19679	+	40.2148i	0.299504	+	1.46942i
$750$	4.17880	+	32.3246i	0.152588	+	1.18033i
$751$	47.3485	+	27.3367i	1.72777	+	0.997530i	0.899009	+	0.437931i	$0.144288\pi$
$751$	47.3485	+	27.3367i	1.72777	+	0.997530i	0.828763	+	0.559599i	$0.189045\pi$
$752$	4.14120	+	4.14120i	0.151014	+	0.151014i
$753$	0.0860062	+	0.665291i	0.00313424	+	0.0242446i
$754$	−6.88029	−	10.3067i	−0.250565	−	0.375348i
$755$		−	67.2221i		−	2.44646i
$756$	0.867745	+	13.7203i	0.0315596	+	0.499003i
$757$	0.0583063	+	0.100989i	0.00211918	+	0.00367052i	0.867083	−	0.498164i	$-0.165992\pi$
$757$	0.0583063	+	0.100989i	0.00211918	+	0.00367052i	−0.864964	+	0.501834i	$0.832659\pi$
$758$	14.6433			0.531867
$759$	20.1372	−	26.1167i	0.730934	−	0.947977i
$760$	−4.29379	+	16.0247i	−0.155752	+	0.581275i
$761$	12.2838	+	12.2838i	0.445288	+	0.445288i	0.893784	−	0.448497i	$-0.148040\pi$
$761$	12.2838	+	12.2838i	0.445288	+	0.445288i	−0.448497	+	0.893784i	$0.648040\pi$
$762$	−5.67369	−	0.760447i	−0.205536	−	0.0275481i
$763$	−3.21825	−	2.12846i	−0.116508	−	0.0770553i
$764$	8.12590	+	14.0745i	0.293985	+	0.509196i
$765$	9.93009	+	0.0464071i	0.359023	+	0.00167785i
$766$	15.6584	+	9.04040i	0.565762	+	0.326643i
$767$	23.0818	−	46.7543i	0.833434	−	1.68820i
$768$	1.59865	+	0.666564i	0.0576864	+	0.0240526i
$769$	−1.17842	+	4.39791i	−0.0424948	+	0.158593i	−0.983913	−	0.178649i	$-0.942827\pi$
$769$	−1.17842	+	4.39791i	−0.0424948	+	0.158593i	0.941418	+	0.337242i	$0.109494\pi$
$770$	38.1916	+	2.32217i	1.37633	+	0.0836854i
$771$	6.15946	+	47.6458i	0.221828	+	1.71592i
$772$	−0.633195	+	2.36312i	−0.0227892	+	0.0850505i
$773$	47.4806	+	12.7224i	1.70776	+	0.457592i	0.974873	−	0.222760i	$-0.0715068\pi$
$773$	47.4806	+	12.7224i	1.70776	+	0.457592i	0.732885	+	0.680353i	$0.238173\pi$
$774$	−3.44398	−	2.00990i	−0.123791	−	0.0722445i
$775$	52.5439	+	14.0791i	1.88743	+	0.505736i
$776$	−3.19159	−	1.84267i	−0.114571	−	0.0661478i
$777$	−1.78639	−	26.2942i	−0.0640866	−	0.943299i
$778$	−32.9725	−	8.83497i	−1.18212	−	0.316749i
$779$	1.72423	+	2.98645i	0.0617769	+	0.107001i
$780$	18.1547	−	15.8326i	0.650043	−	0.566896i
$781$	2.36347	−	4.09364i	0.0845715	−	0.146482i
$782$	−1.12794	−	4.20952i	−0.0403350	−	0.150532i
$783$	14.0920	+	10.9710i	0.503606	+	0.392070i
$784$	5.59346	+	4.20870i	0.199767	+	0.150311i
$785$	−55.2393	+	55.2393i	−1.97158	+	1.97158i
$786$	19.8387	+	2.65899i	0.707622	+	0.0948429i
$787$	−39.7936	−	10.6627i	−1.41849	−	0.380083i	−0.533542	−	0.845773i	$-0.679139\pi$
$787$	−39.7936	−	10.6627i	−1.41849	−	0.380083i	−0.884948	+	0.465690i	$0.845806\pi$
$788$	17.2752	−	4.62888i	0.615404	−	0.164897i
$789$	−9.77372	−	12.7992i	−0.347954	−	0.455663i
$790$	47.2092	−	27.2563i	1.67963	−	0.969734i
$791$	3.84126	+	18.8458i	0.136579	+	0.670081i
$792$	−10.8506	−	2.96184i	−0.385561	−	0.105244i
$793$	10.9772	+	2.18842i	0.389810	+	0.0777131i
$794$	−5.37307	−	3.10214i	−0.190683	−	0.110091i
$795$	31.1440	+	4.17424i	1.10456	+	0.148045i
$796$	4.41771	−	7.65170i	0.156582	−	0.271207i
$797$	3.17850	−	5.50533i	0.112588	−	0.195009i	−0.804225	−	0.594325i	$-0.797419\pi$
$797$	3.17850	−	5.50533i	0.112588	−	0.195009i	0.916813	+	0.399316i	$0.130753\pi$
$798$	12.9600	−	14.8493i	0.458777	−	0.525659i
$799$	−4.85446	+	1.30075i	−0.171739	+	0.0460172i
$800$	−6.98519	−	6.98519i	−0.246964	−	0.246964i
$801$	0.0164021	−	3.50968i	0.000579540	−	0.124009i
$802$	−6.77236	−	11.7301i	−0.239140	−	0.414203i
$803$	−9.32473	+	16.1509i	−0.329063	+	0.569953i
$804$	22.4123	−	9.22217i	0.790420	−	0.325241i
$805$	−51.7322	−	3.14549i	−1.82332	−	0.110864i
$806$	−6.37386	−	18.8035i	−0.224510	−	0.662324i
$807$	−9.87633	+	23.6869i	−0.347663	+	0.833817i
$808$	−12.1948	−	12.1948i	−0.429013	−	0.429013i
$809$			7.31064i			0.257028i	0.991708	+	0.128514i	$0.0410208\pi$
$809$			7.31064i			0.257028i	−0.991708	+	0.128514i	$0.958979\pi$
$810$	−17.6380	+	29.9009i	−0.619735	+	1.05061i
$811$	−3.16405	−	3.16405i	−0.111105	−	0.111105i	0.649369	−	0.760474i	$-0.275033\pi$
$811$	−3.16405	−	3.16405i	−0.111105	−	0.111105i	−0.760474	+	0.649369i	$0.775033\pi$
$812$	8.91019	−	1.81612i	0.312686	−	0.0637333i
$813$	−41.0964	−	31.6872i	−1.44131	−	1.11132i
$814$	20.8273	+	5.58067i	0.729998	+	0.195602i
$815$	−20.5732	+	11.8780i	−0.720648	+	0.416067i
$816$	−1.18130	+	0.902066i	−0.0413538	+	0.0315786i
$817$	1.47961	+	5.52199i	0.0517651	+	0.193190i
$818$	15.3747			0.537563
$819$	−27.6459	+	7.39631i	−0.966025	+	0.258448i
$820$	−3.09272			−0.108003
$821$	0.210539	+	0.785743i	0.00734787	+	0.0274226i	0.969502	−	0.245082i	$-0.0788148\pi$
$821$	0.210539	+	0.785743i	0.00734787	+	0.0274226i	−0.962155	+	0.272504i	$0.912148\pi$
$822$	−27.1990	+	20.7698i	−0.948676	+	0.724429i
$823$	35.8641	−	20.7061i	1.25014	−	0.721771i	0.279006	−	0.960289i	$-0.409995\pi$
$823$	35.8641	−	20.7061i	1.25014	−	0.721771i	0.971138	+	0.238519i	$0.0766618\pi$
$824$	−18.1361	−	4.85955i	−0.631801	−	0.169291i
$825$	50.8019	+	39.1706i	1.76869	+	1.36374i
$826$	25.3630	+	28.6470i	0.882492	+	0.996756i
$827$	15.6164	+	15.6164i	0.543037	+	0.543037i	0.924418	−	0.381381i	$-0.124551\pi$
$827$	15.6164	+	15.6164i	0.543037	+	0.543037i	−0.381381	+	0.924418i	$0.624551\pi$
$828$	14.6977	+	4.01194i	0.510779	+	0.139425i
$829$		−	36.3249i		−	1.26162i	−0.775939	−	0.630808i	$-0.782724\pi$
$829$		−	36.3249i		−	1.26162i	0.775939	−	0.630808i	$-0.217276\pi$
$830$	−18.1512	−	18.1512i	−0.630037	−	0.630037i
$831$	12.3683	−	29.6635i	0.429052	−	1.02902i
$832$	−0.704936	+	3.53597i	−0.0244392	+	0.122588i
$833$	−5.52775	+	2.35106i	−0.191525	+	0.0814595i
$834$	−7.67061	+	3.15629i	−0.265612	+	0.109294i
$835$	−34.1362	+	59.1257i	−1.18133	+	2.04613i
$836$	8.06258	+	13.9648i	0.278850	+	0.482983i
$837$	17.2591	+	22.8219i	0.596561	+	0.788842i
$838$	16.1777	+	16.1777i	0.558850	+	0.558850i
$839$	47.9933	−	12.8598i	1.65691	−	0.443968i	0.695376	−	0.718646i	$-0.255238\pi$
$839$	47.9933	−	12.8598i	1.65691	−	0.443968i	0.961536	+	0.274677i	$0.0885711\pi$
$840$	5.72174	+	16.7246i	0.197419	+	0.577053i
$841$	−8.59359	+	14.8845i	−0.296331	+	0.513260i
$842$	10.6444	−	18.4367i	0.366831	−	0.635369i
$843$	−47.7193	−	6.39584i	−1.64354	−	0.220284i
$844$	−17.1820	−	9.92000i	−0.591427	−	0.341461i
$845$	39.7560	+	30.5604i	1.36765	+	1.05131i
$846$	4.62661	−	16.9495i	0.159066	−	0.582736i
$847$	6.05482	−	5.36071i	0.208046	−	0.184196i
$848$	−4.07315	+	2.35163i	−0.139873	+	0.0807554i
$849$	−23.3844	−	30.6230i	−0.802549	−	1.05098i
$850$	8.18829	−	2.19405i	0.280856	−	0.0752552i
$851$	−28.2115	−	7.55926i	−0.967079	−	0.259128i
$852$	2.16438	+	0.290093i	0.0741506	+	0.00993843i
$853$	10.0034	−	10.0034i	0.342509	−	0.342509i	−0.514801	−	0.857310i	$-0.672134\pi$
$853$	10.0034	−	10.0034i	0.342509	−	0.342509i	0.857310	+	0.514801i	$0.172134\pi$
$854$	−4.53091	+	6.85078i	−0.155044	+	0.234429i
$855$	48.1336	−	12.6566i	1.64614	−	0.432846i
$856$	−4.01488	−	14.9837i	−0.137226	−	0.512133i
$857$	2.65429	−	4.59736i	0.0906687	−	0.157043i	−0.817124	−	0.576462i	$-0.804433\pi$
$857$	2.65429	−	4.59736i	0.0906687	−	0.157043i	0.907793	+	0.419419i	$0.137766\pi$
$858$	1.59601	−	23.3593i	0.0544870	−	0.797475i
$859$	−15.0092	−	25.9966i	−0.512106	−	0.886993i	−0.999901	−	0.0140355i	$-0.995532\pi$
$859$	−15.0092	−	25.9966i	−0.512106	−	0.886993i	0.487796	−	0.872958i	$-0.337801\pi$
$860$	−4.95235	−	1.32698i	−0.168874	−	0.0452496i
$861$	3.29921	+	1.61722i	0.112437	+	0.0551148i
$862$	14.2660	+	8.23648i	0.485902	+	0.280536i
$863$	−14.8968	−	3.99159i	−0.507093	−	0.135875i	−0.00380322	−	0.999993i	$-0.501211\pi$
$863$	−14.8968	−	3.99159i	−0.507093	−	0.135875i	−0.503290	+	0.864118i	$0.667877\pi$
$864$	−0.642104	−	5.15633i	−0.0218448	−	0.175422i
$865$	−8.83091	−	2.36623i	−0.300260	−	0.0804544i
$866$	9.12643	−	34.0603i	0.310129	−	1.15742i
$867$	3.61157	+	27.9369i	0.122655	+	0.948787i
$868$	14.5423	+	0.884219i	0.493597	+	0.0300123i
$869$	13.7136	−	51.1799i	0.465202	−	1.73616i
$870$	21.1939	+	8.83689i	0.718541	+	0.299599i
$871$	28.0105	+	41.9599i	0.949099	+	1.42176i
$872$	1.26297	+	0.729174i	0.0427695	+	0.0246930i
$873$	−0.0516684	+	11.0559i	−0.00174871	+	0.374185i
$874$	−10.9211	−	18.9159i	−0.369412	−	0.639841i
$875$	3.02167	−	49.6958i	0.102151	−	1.68002i
$876$	−8.53928	−	1.14452i	−0.288515	−	0.0386698i
$877$	−35.1833	−	35.1833i	−1.18806	−	1.18806i	−0.977604	−	0.210451i	$-0.932507\pi$
$877$	−35.1833	−	35.1833i	−1.18806	−	1.18806i	−0.210451	−	0.977604i	$-0.567493\pi$
$878$	−10.4557	+	39.0211i	−0.352862	+	1.31690i
$879$	−0.477925	+	0.619840i	−0.0161200	+	0.0209067i
$880$	−14.4617			−0.487505
$881$	−21.7730	−	37.7119i	−0.733550	−	1.27055i	−0.955356	−	0.295456i	$-0.904529\pi$
$881$	−21.7730	−	37.7119i	−0.733550	−	1.27055i	0.221806	−	0.975091i	$-0.428805\pi$
$882$	2.64172	−	20.8332i	0.0889514	−	0.701490i
$883$			3.45829i			0.116381i	0.998306	+	0.0581904i	$0.0185331\pi$
$883$			3.45829i			0.116381i	−0.998306	+	0.0581904i	$0.981467\pi$
$884$	−2.32535	−	2.04106i	−0.0782100	−	0.0686481i
$885$	12.3872	+	95.8194i	0.416390	+	3.22093i
$886$	11.5439	+	11.5439i	0.387826	+	0.387826i
$887$	−23.0347	−	13.2991i	−0.773429	−	0.446539i	0.0606677	−	0.998158i	$-0.480677\pi$
$887$	−23.0347	−	13.2991i	−0.773429	−	0.446539i	−0.834096	+	0.551619i	$0.814010\pi$
$888$	1.27712	+	9.87898i	0.0428572	+	0.331517i
$889$	8.29333	+	2.77161i	0.278149	+	0.0929567i
$890$	−1.16796	−	4.35889i	−0.0391501	−	0.146110i
$891$	8.42828	+	32.6733i	0.282358	+	1.09460i
$892$	1.25289	+	4.67584i	0.0419498	+	0.156559i
$893$	−21.8140	+	12.5943i	−0.729979	+	0.421454i
$894$	−11.1983	+	1.44767i	−0.374527	+	0.0484174i
$895$	−35.0514	−	9.39201i	−1.17164	−	0.313940i
$896$	−2.20678	−	1.45950i	−0.0737232	−	0.0487584i
$897$	−2.16187	+	31.6412i	−0.0721828	+	1.05647i
$898$	5.29600	+	9.17294i	0.176730	+	0.306105i
$899$	13.3828	−	13.3828i	0.446341	−	0.446341i
$900$	−7.80397	+	28.5897i	−0.260132	+	0.952990i
$901$		−	4.03604i		−	0.134460i
$902$	−2.12562	+	2.12562i	−0.0707753	+	0.0707753i
$903$	4.58911	+	4.00522i	0.152716	+	0.133285i
$904$	−1.88149	−	7.02181i	−0.0625774	−	0.233542i
$905$	24.3384	−	90.8321i	0.809036	−	3.01936i
$906$	11.6165	−	27.8603i	0.385931	−	0.925597i
$907$			3.69478i			0.122683i	0.998117	+	0.0613416i	$0.0195379\pi$
$907$			3.69478i			0.122683i	−0.998117	+	0.0613416i	$0.980462\pi$
$908$	9.71058	−	2.60194i	0.322257	−	0.0863485i
$909$	−13.6243	+	49.9122i	−0.451888	+	1.65548i
$910$	−31.7871	+	18.5345i	−1.05373	+	0.614414i
$911$		−	36.0850i		−	1.19555i	−0.801664	−	0.597774i	$-0.796052\pi$
$911$		−	36.0850i		−	1.19555i	0.801664	−	0.597774i	$-0.203948\pi$
$912$	−4.54874	+	5.89944i	−0.150624	+	0.195350i
$913$	−24.9505			−0.825742
$914$	0.801092	+	1.38753i	0.0264978	+	0.0458955i
$915$	−19.1804	+	7.89231i	−0.634083	+	0.260912i
$916$	−1.65457	+	0.443341i	−0.0546686	+	0.0146484i
$917$	−28.9985	−	9.69123i	−0.957616	−	0.320033i
$918$	4.10752	+	1.73522i	0.135568	+	0.0572709i
$919$	−3.24432			−0.107020			−0.0535101	−	0.998567i	$-0.517041\pi$
$919$	−3.24432			−0.107020			−0.0535101	+	0.998567i	$0.517041\pi$
$920$	19.5890			0.645831
$921$	0.613595	−	4.57803i	0.0202186	−	0.150851i
$922$	9.18278	−	5.30168i	0.302419	−	0.174602i
$923$	0.295351	+	4.53621i	0.00972160	+	0.149311i
$924$	15.4273	+	7.56221i	0.507520	+	0.248778i
$925$	14.7042	−	54.8767i	0.483470	−	1.80433i
$926$	−16.9341	−	9.77689i	−0.556488	−	0.321288i
$927$	14.3242	+	54.4758i	0.470469	+	1.78922i
$928$	−3.31987	+	0.889555i	−0.108980	+	0.0292011i
$929$	−3.29076	+	3.29076i	−0.107966	+	0.107966i	−0.759026	−	0.651060i	$-0.774325\pi$
$929$	−3.29076	+	3.29076i	−0.107966	+	0.107966i	0.651060	+	0.759026i	$0.274325\pi$
$930$	29.1348	+	22.4643i	0.955368	+	0.736633i
$931$	−23.7111	+	18.5525i	−0.777099	+	0.608033i
$932$	−12.9819	−	7.49512i	−0.425237	−	0.245511i
$933$	2.73739	+	21.1747i	0.0896180	+	0.693230i
$934$	−11.7460	+	11.7460i	−0.384342	+	0.384342i
$935$	6.20506	−	10.7475i	0.202927	−	0.351480i
$936$	10.2602	−	3.42456i	0.335366	−	0.111935i
$937$	34.1925			1.11702			0.558510	−	0.829498i	$-0.311373\pi$
$937$	34.1925			1.11702			0.558510	+	0.829498i	$0.311373\pi$
$938$	−36.2745	+	7.39365i	−1.18440	+	0.241411i
$939$	−10.5140	−	4.38384i	−0.343110	−	0.143061i
$940$		−	22.5903i		−	0.736814i
$941$	−4.80425	−	17.9297i	−0.156614	−	0.584491i	−0.998962	−	0.0455568i	$-0.985494\pi$
$941$	−4.80425	−	17.9297i	−0.156614	−	0.584491i	0.842348	−	0.538934i	$-0.181173\pi$
$942$	−32.4398	+	13.3483i	−1.05694	+	0.434910i
$943$	2.87924	−	2.87924i	0.0937610	−	0.0937610i
$944$	−10.2258	−	10.2258i	−0.332821	−	0.332821i
$945$	35.0554	−	39.7890i	1.14035	−	1.29434i
$946$	−4.31576	+	2.49171i	−0.140318	+	0.0810124i
$947$	−23.2940	+	6.24161i	−0.756953	+	0.202825i	−0.616600	−	0.787277i	$-0.711490\pi$
$947$	−23.2940	+	6.24161i	−0.756953	+	0.202825i	−0.140353	+	0.990102i	$0.544824\pi$
$948$	24.2760	−	3.13831i	0.788449	−	0.101928i
$949$	−1.16527	−	17.8970i	−0.0378262	−	0.580961i
$950$	36.7950	−	21.2436i	1.19379	−	0.689233i
$951$	0.684719	−	0.281747i	0.0222035	−	0.00913627i
$952$	2.03151	−	1.01378i	0.0658416	−	0.0328568i
$953$	−0.921008	+	1.59523i	−0.0298344	+	0.0516747i	−0.880557	−	0.473940i	$-0.842831\pi$
$953$	−0.921008	+	1.59523i	−0.0298344	+	0.0516747i	0.850723	+	0.525615i	$0.176165\pi$
$954$	12.1863	+	7.11193i	0.394548	+	0.230257i
$955$	16.2248	−	60.5516i	0.525021	−	1.95940i
$956$	−2.70678	+	10.1019i	−0.0875436	+	0.326717i
$957$	20.6401	−	8.49295i	0.667199	−	0.274538i
$958$	−2.04088	+	3.53491i	−0.0659380	+	0.114208i
$959$	46.7748	−	23.3420i	1.51044	−	0.753752i
$960$	−2.54228	−	6.17839i	−0.0820516	−	0.199407i
$961$	−0.586446	+	0.338585i	−0.0189176	+	0.0109221i
$962$	−19.6383	+	6.65684i	−0.633164	+	0.214625i
$963$	−33.0600	+	32.7524i	−1.06534	+	1.05543i
$964$	7.98507	−	2.13959i	0.257182	−	0.0689117i
$965$	8.17245	−	4.71837i	0.263081	−	0.151890i
$966$	−20.8969	−	10.2433i	−0.672347	−	0.329574i
$967$	−3.86855	−	3.86855i	−0.124404	−	0.124404i	0.642163	−	0.766568i	$-0.278037\pi$
$967$	−3.86855	−	3.86855i	−0.124404	−	0.124404i	−0.766568	+	0.642163i	$0.778037\pi$
$968$	−2.16132	+	2.16132i	−0.0694673	+	0.0694673i
$969$	−2.43256	−	5.91174i	−0.0781449	−	0.189913i
$970$	3.67920	+	13.7310i	0.118132	+	0.440874i
$971$			41.9582i			1.34650i	0.739413	+	0.673252i	$0.235103\pi$
$971$			41.9582i			1.34650i	−0.739413	+	0.673252i	$0.764897\pi$
$972$	−12.4772	+	9.34452i	−0.400206	+	0.299726i
$973$	12.4150	−	2.53048i	0.398005	−	0.0811235i
$974$	−5.58134			−0.178838
$975$	−61.5481	−	4.20524i	−1.97112	−	0.134675i
$976$	1.55221	−	2.68851i	0.0496852	−	0.0860572i
$977$	7.26575	−	7.26575i	0.232452	−	0.232452i	−0.581263	−	0.813715i	$-0.697441\pi$
$977$	7.26575	−	7.26575i	0.232452	−	0.232452i	0.813715	+	0.581263i	$0.197441\pi$
$978$	−10.5792	+	1.36764i	−0.338285	+	0.0437322i
$979$	−3.79858	−	2.19311i	−0.121403	−	0.0700922i
$980$	−3.77694	−	26.7354i	−0.120650	−	0.854032i
$981$	0.0204461	−	4.37500i	0.000652792	−	0.139683i
$982$	18.9606	−	18.9606i	0.605056	−	0.605056i
$983$	20.7833	−	5.56888i	0.662885	−	0.177620i	0.0883374	−	0.996091i	$-0.471845\pi$
$983$	20.7833	−	5.56888i	0.662885	−	0.177620i	0.574548	+	0.818471i	$0.305178\pi$
$984$	−1.28178	−	0.534445i	−0.0408618	−	0.0170375i
$985$	−59.7435	−	34.4929i	−1.90359	−	1.09904i
$986$	0.763360	−	2.84890i	0.0243103	−	0.0907274i
$987$	−11.8127	+	24.0985i	−0.376003	+	0.767065i
$988$	−13.9051	−	6.86471i	−0.442380	−	0.218395i
$989$	5.84589	−	3.37512i	0.185888	−	0.107323i
$990$	21.5168	+	37.6736i	0.683847	+	1.19735i
$991$	−42.8493			−1.36115			−0.680577	−	0.732677i	$-0.738271\pi$
$991$	−42.8493			−1.36115			−0.680577	+	0.732677i	$0.738271\pi$
$992$	−5.50662			−0.174835
$993$	21.1637	+	2.83657i	0.671608	+	0.0900160i
$994$	−3.16372	−	1.05731i	−0.100347	−	0.0335357i
$995$	−32.9194	+	8.82072i	−1.04361	+	0.279636i
$996$	−4.38614	−	10.6595i	−0.138980	−	0.337758i
$997$	−18.8867	−	32.7127i	−0.598147	−	1.03602i	−0.993095	−	0.117317i	$-0.962571\pi$
$997$	−18.8867	−	32.7127i	−0.598147	−	1.03602i	0.394948	−	0.918704i	$-0.370763\pi$
$998$	−0.687588			−0.0217652
$999$	23.8352	−	18.0253i	0.754111	−	0.570296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.5	✓	152
3.2	odd	2	inner	546.2.bw.a.11.24	yes	152
7.2	even	3		546.2.ch.a.401.10	yes	152
13.6	odd	12		546.2.ch.a.305.35	yes	152
21.2	odd	6		546.2.ch.a.401.35	yes	152
39.32	even	12		546.2.ch.a.305.10	yes	152
91.58	odd	12	inner	546.2.bw.a.149.24	yes	152
273.149	even	12	inner	546.2.bw.a.149.5	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.5	✓	152	1.1	even	1	trivial
546.2.bw.a.11.24	yes	152	3.2	odd	2	inner
546.2.bw.a.149.5	yes	152	273.149	even	12	inner
546.2.bw.a.149.24	yes	152	91.58	odd	12	inner
546.2.ch.a.305.10	yes	152	39.32	even	12
546.2.ch.a.305.35	yes	152	13.6	odd	12
546.2.ch.a.401.10	yes	152	7.2	even	3
546.2.ch.a.401.35	yes	152	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.37659 + 1.05119i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(3.72584 + 0.998336i) q^{5} +(1.37166 + 1.05761i) q^{6} +(-1.75384 - 1.98092i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.789991 - 2.89412i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.37659 + 1.05119i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(3.72584 + 0.998336i) q^{5} +(1.37166 + 1.05761i) q^{6} +(-1.75384 - 1.98092i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.789991 - 2.89412i) q^{9} -3.85727i q^{10} +(-2.65109 - 2.65109i) q^{11} +(0.666564 - 1.59865i) q^{12} +(3.53597 + 0.704936i) q^{13} +(-1.45950 + 2.20678i) q^{14} +(-6.17839 + 2.54228i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.429068 + 0.743168i) q^{17} +(-2.99997 - 0.0140200i) q^{18} +(3.04123 + 3.04123i) q^{19} +(-3.72584 + 0.998336i) q^{20} +(4.49664 + 0.883296i) q^{21} +(-1.87460 + 3.24691i) q^{22} +(2.53923 - 4.39808i) q^{23} +(-1.71670 - 0.230090i) q^{24} +(8.55508 + 4.93928i) q^{25} +(-0.234260 - 3.59793i) q^{26} +(1.95478 + 4.81444i) q^{27} +(2.50933 + 0.838611i) q^{28} +(2.97651 - 1.71849i) q^{29} +(4.05473 + 5.30988i) q^{30} +(5.31898 - 1.42522i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(6.43627 + 0.862655i) q^{33} +(0.606794 - 0.606794i) q^{34} +(-4.55689 - 9.13152i) q^{35} +(0.762906 + 2.90137i) q^{36} +(-1.48849 - 5.55513i) q^{37} +(2.15047 - 3.72473i) q^{38} +(-5.60859 + 2.74657i) q^{39} +(1.92864 + 3.34050i) q^{40} +(0.774470 + 0.207519i) q^{41} +(-0.310618 - 4.57204i) q^{42} +(1.15111 + 0.664595i) q^{43} +(3.62146 + 0.970367i) q^{44} +(5.83268 - 9.99434i) q^{45} +(-4.90542 - 1.31440i) q^{46} +(-1.51578 + 5.65698i) q^{47} +(0.222065 + 1.71776i) q^{48} +(-0.848111 + 6.94843i) q^{49} +(2.55676 - 9.54195i) q^{50} +(-1.37186 - 0.572003i) q^{51} +(-3.41471 + 1.15749i) q^{52} +(-4.07315 - 2.35163i) q^{53} +(4.14446 - 3.13424i) q^{54} +(-7.23086 - 12.5242i) q^{55} +(0.160574 - 2.64087i) q^{56} +(-7.38344 - 0.989606i) q^{57} +(-2.43031 - 2.43031i) q^{58} +(3.74289 - 13.9687i) q^{59} +(4.07951 - 5.29087i) q^{60} +3.10443 q^{61} +(-2.75331 - 4.76887i) q^{62} +(-7.11854 + 3.51090i) q^{63} +1.00000i q^{64} +(12.4707 + 6.15656i) q^{65} +(-0.832567 - 6.44023i) q^{66} +(9.89409 + 9.89409i) q^{67} +(-0.743168 - 0.429068i) q^{68} +(1.12775 + 8.72357i) q^{69} +(-7.64096 + 6.76503i) q^{70} +(0.326314 + 1.21782i) q^{71} +(2.60506 - 1.48784i) q^{72} +(-1.28743 - 4.80475i) q^{73} +(-4.98059 + 2.87555i) q^{74} +(-16.9690 + 2.19368i) q^{75} +(-4.15440 - 1.11317i) q^{76} +(-0.602025 + 9.90119i) q^{77} +(4.10460 + 4.70662i) q^{78} +(7.06620 + 12.2390i) q^{79} +(2.72750 - 2.72750i) q^{80} +(-7.75183 - 4.57265i) q^{81} -0.801790i q^{82} +(4.70571 - 4.70571i) q^{83} +(-4.33585 + 1.48336i) q^{84} +(0.856708 + 3.19728i) q^{85} +(0.344020 - 1.28390i) q^{86} +(-2.29097 + 5.49454i) q^{87} -3.74921i q^{88} +(1.13004 - 0.302794i) q^{89} +(-11.1634 - 3.04721i) q^{90} +(-4.80509 - 8.24082i) q^{91} +5.07846i q^{92} +(-5.82387 + 7.55321i) q^{93} +5.85654 q^{94} +(8.29497 + 14.3673i) q^{95} +(1.60175 - 0.659086i) q^{96} +(-3.55976 + 0.953834i) q^{97} +(6.93118 - 0.979174i) q^{98} +(-9.76690 + 5.57823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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